Macroeconomic Crises since 1870 - Thomas Pikettypiketty.pse.ens.fr/files/BarroUrsua08.pdf ·...
Transcript of Macroeconomic Crises since 1870 - Thomas Pikettypiketty.pse.ens.fr/files/BarroUrsua08.pdf ·...
1
ROBERT J. BARROHarvard University
JOSÉ F. URSÚAHarvard University
Macroeconomic Crises since 1870
ABSTRACT We build on Angus Maddison’s data by assembling inter-national time series from before 1914 on real per capita personal consumerexpenditure, C, and by improving the GDP data. We have full annual data onC for twenty-four countries and GDP for thirty-six. For samples starting at1870, we apply a peak-to-trough method to isolate economic crises, defined ascumulative declines in C or GDP of at least 10 percent. We find 95 crises for Cand 152 for GDP, implying disaster probabilities of 31⁄2 percent a year, withmean size of 21–22 percent and average duration of 31⁄2 years. Simulation of aLucas-tree model with i.i.d. shocks and Epstein-Zin-Weil preferences accordswith the observed average equity premium of around 7 percent on leveredequity, using a coefficient of relative risk aversion of 3.5. This result is robustto several perturbations, except for limiting the sample to nonwar crises.
An earlier study by Barro used Thomas Rietz’s insight on rare eco-nomic disasters to explain the equity premium puzzle introduced by
Rajnish Mehra and Edward Prescott.1 Key parameters were the probabilityp of disaster and the distribution of disaster sizes b. Because large macro-economic disasters are rare, pinning down p and the b distribution fromhistorical data requires long time series for many countries, along with theassumption of rough parameter stability over time and across countries.Barro’s 2006 study relied on long-term international GDP data for thirty-five countries from Angus Maddison’s 2003 dataset.2 Using the definitionof an economic disaster as a peak-to-trough fall in GDP per capita of atleast 15 percent, Barro found sixty disasters, corresponding to p = 1.7 per-cent a year. The average disaster size was 29 percent, and the empiricalsize distribution was used to calibrate a model of asset pricing.
1. Barro (2006); Rietz (1988); Mehra and Prescott (1985).2. Maddison (2003).
Ftn. 1
Ftn. 2
11302-04_Barro.qxd 8/15/08 5:38 PM Page 1
The underlying asset pricing theory relates to consumption, rather thanGDP. This distinction is especially important for wars. For example, in theUnited Kingdom during the two world wars, GDP increased while con-sumer expenditure fell sharply, the difference representing mostly addedmilitary spending. Maddison’s 2003 dataset provides national accountsinformation only for GDP. Our initial idea was to add consumption, whichwe approximate by real personal consumer expenditure, C, because of dif-ficulties in most cases in separating durable goods consumption from thatof nondurable goods and services. (We discuss later the breakdown of Cinto durables versus nondurables for a subset of countries with availabledata for crisis periods.) We have not assembled data on government con-sumption, some of which may substitute for C and thereby affect assetpricing. However, this substitution is probably unimportant for militaryexpenditure, which is the type of government spending that moves sharplyduring some disaster events.
Maddison’s 2003 dataset, with updates available on the Internet atwww.ggdc.net/maddison, represents a monumental and widely usedresource for international studies using long-term GDP data. Althoughmuch of the information is sound, close examination revealed many prob-lems. For our purposes the most important shortcoming is that Maddisontends to fill in missing data with doubtful assumptions, and this practiceapplies especially to major crises.
As examples of problems, Maddison assumed that Belgium’s GDP dur-ing World Wars I and II moved in tandem with France’s; that Mexico’sGDP between 1910 and 1919, the period including its revolution andcivil war, followed a smooth trend, with no crisis; that GDP for Colombiamoved over more than a decade with the average of Brazil and Chile; andthat GDP in Germany for the crucial years 1944–46 followed a lineartrend. There were also mismatches between originally cited works andpublished series for GDP in Japan and Austria at the end of World War II,in Greece during World War II and its civil war, and in South Korea duringWorld War II and the Korean War.
Given these and analogous problems, our project expanded to estimat-ing long-term GDP for many countries. The Maddison information wasoften usable, but superior estimates or longer time series could often beconstructed. In addition, results from recent major long-term nationalaccounts projects for several countries are now available and have not beenincorporated into Maddison’s Internet updates. These studies coverArgentina, Brazil, Colombia, Greece, Sweden, and Taiwan. Table A1 inappendix A summarizes the key differences, by country and time period,
2 Brookings Papers on Economic Activity, Spring 2008
11302-04_Barro.qxd 8/15/08 5:38 PM Page 2
between Maddison’s and our GDP data. Details and a complete list of datasources are available on the Internet.
The first section of the paper describes the long-term data that we haveassembled on real per capita personal consumer expenditure, C, and realper capita GDP. Our main analysis uses annual data from before 1914 fortwenty-four countries on C and thirty-six countries on GDP. The secondsection discusses the long-term data that we use on rates of return forstocks, bills, and bonds. This information comes mostly from GlobalFinancial Data. The third section describes our measurement of C andGDP crises, based primarily on peak-to-trough fractional declines duringthe crises. The fourth section discusses the limited information availableon the breakdown of C into durables versus nondurables and services.
The fifth section compares disaster sizes and timing based on C withthose based on GDP. The sixth section uses the crises data to measuredisaster probabilities and frequency distributions of disaster sizes. Theseventh section summarizes a representative-agent Lucas-tree modelthat relates disaster experience to expected rates of return and the equitypremium. The eighth section simulates the Lucas-tree model using theempirically estimated disaster probability and the frequency distribution ofdisaster sizes. The simulated model with a reasonable coefficient of rela-tive risk aversion accords reasonably well with observed equity premia.The ninth section modifies the simulation to use observed real stock-pricechanges to gauge crisis returns on stocks. We also discuss the low averagereal bill returns observed during crises. The final section concludes withplans for additional research.
Long-Term Data on Personal Consumer Expenditure and GDP
We are dealing with national accounts data for forty-two countries. Thissample is the universe of countries that seem to be promising for con-structing reasonably accurate annual data since before World War I. Thecurrent study focuses on the countries for which we have thus far assem-bled annual data from before 1914 to 2006 on C (twenty-four countries)and GDP (thirty-six countries).
Table 1 shows a list of included countries and starting years. The toppanel applies to twenty-one “OECD countries” (not including Turkey orrecently acceding members); seventeen of these are in our C sample, andall twenty-one are in our GDP sample. The bottom panel covers eighteen“non-OECD” countries, of which seven are in our C sample, and fifteenare in our GDP sample. The three countries that we are studying that are
ROBERT J. BARRO and JOSÉ F. URSÚA 3
TAB. 1
11302-04_Barro.qxd 8/15/08 5:38 PM Page 3
Table 1. Starting Dates and Missing Values for Consumer Expenditure and GDPa
Starting dates Missing values
Country C GDP C GDP
OECD countriesb
Australia 1901 1820Austria 1913c 1870 1919–23,
1945–46Belgium 1913 1846Canada 1871 1870Denmark 1844 1818Finland 1860 1860France 1824 1820Germany 1851 1851Greece 1938c 1833e 1944Iceland 1945c 1870Italy 1861 1861Japan 1874 1870Netherlands 1814 1807New Zealand 1939c 1870 1940–43,
1945–46Norway 1830 1830Portugal 1910 1865Spain 1850 1850Sweden 1800 1800Switzerland 1851 1851United Kingdom 1830 1830United States 1869 1869
Non-OECD countriesArgentina 1875 1875Brazil 1901 1850Chile 1900 1860Colombia 1925c 1905India 1919c 1872Indonesia 1960c 1880Malaysia 1900c 1900d 1940–46 1943–46Mexico 1900 1895Peru 1896 1896Philippines 1950c 1902f 1941–45Singapore 1900c 1900d 1940–47 1940–49South Africa 1946c 1911South Korea 1911 1911Sri Lanka 1960c 1870Taiwan 1901 1901Turkey 1923c 1923d
Uruguay 1960c 1870Venezuela 1923c 1883
Source: Authors’ construction; for details on sources and procedures see the online appendix at www.economics.harvard.edu/faculty/barro/data_sets_barro.
a. C represents real per capita personal consumer expenditure; GDP represents real per capita GDP.Missing values apply to each period between country starting date and 2006. Criterion for inclusion insamples is presence of continuous annual data back before World War I.
b. Excludes recently acceding members and Turkey.c. Excluded from analysis for C sample because of insufficient coverage.d. Excluded from analysis for GDP sample because of insufficient coverage.e. Included in the GDP sample with data for log(GDP) in 1944 interpolated between values for 1943
and 1945. This interpolation does not affect the estimated decline in GDP during World War II.f. Included in part of the analysis of GDP data despite the gap in information for 1941–45. This gap
does not hinder estimating the cumulative contraction in GDP associated with World War II.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 4
omitted from table 1 because of insufficient progress with the data areEgypt, Ireland, and Russia. We start our analysis of growth rates in 1870,although earlier data are available in some cases.
Our present analysis uses growth rates of C and GDP and does notinvolve comparisons of levels across countries. Therefore we can useindexes of both variables, for example, setting their values at 100 for eachcountry in 2000. However, the level comparisons matter for the construc-tion of measures of C and GDP for groups of countries, such as the total ofthe OECD. To facilitate this analysis (and to allow for other uses of thedata that depend on comparability of levels across countries), we set thelevel of per capita GDP for each country in 2000 to the purchasing powerparity (PPP)-adjusted value in 2000 international dollars given in theWorld Bank’s World Development Indicators (WDI). For per capita con-sumer expenditure, we set the level for each country in 2000 to the valuegiven by the WDI for PPP-adjusted per capita GDP multiplied by the shareof nominal personal consumer expenditure in the country’s nominal GDP.
Sample selection issues particularly affect disaster studies becausedata tend to be absent during the worst crises, especially wars. As exam-ples, Malaysia and Singapore have data on C and GDP since 1900 but aremissing information during World War II. Inclusion of the incompleteMalaysian and Singaporean time series since 1900 in our analysis wouldbias downward the estimated disaster probabilities, since the missing peri-ods almost surely contain crises. We take the approach of excluding caseswith these kinds of selected gaps in the data. In addition to Malaysia andSingapore, we omit Turkey (whose C and GDP data start in 1923, after theOttoman Empire’s crisis during World War I), India for C (where the datastart in 1919), and Austria for C (where the data start in 1913 but informa-tion is missing toward the ends of World Wars I and II). More broadly, ourmain response to this selection issue has been to try to expand the set ofcountries with at least roughly estimated full time series.
The construction of estimates of C relied on various procedures. Inmany cases we used existing long-term national accounts studies. Some-times (for example, Canada before 1926) we estimated C as a residual,starting from GDP and subtracting estimates of the other components ofGDP. Sometimes (for example, Switzerland before 1948 and Germanyaround World War I) we constructed C from quantities of specific con-sumption items, using estimates of expenditure shares to calculate changesin C. The details of our procedures are in our Internet report.
One issue is the treatment of border changes. An illustration is thereunification of Germany in late 1990. We have data on per capita C and
ROBERT J. BARRO and JOSÉ F. URSÚA 5
11302-04_Barro.qxd 8/15/08 5:38 PM Page 5
GDP for West Germany up to 1990 (ignoring, for now, the previous borderchanges) and also after 1990. We have data for unified Germany from1991 on. Since per capita C and GDP in East Germany (not well measuredbefore 1991) were much lower than in the West, the raw data on per capitaquantities would show sharp drops in 1991 if we combined the West Ger-man values up to 1990 with the unified Germany values thereafter. That is,this approach would treat the unification as a disaster event from the per-spective of West Germans leading up to 1990. This perspective may ormay not be accurate for this particular border change,3 but we do not wantto apply this approach to border changes in general. This procedure wouldimply that the initially richer part inevitably regards the coming combina-tion as a disaster, and vice versa for the poorer part.
Even without border changes, the use of per capita C or GDP as a macrovariable neglects the distribution of expenditure and income within a coun-try. This macroeconomic approach, valid under some conditions,4 assumesthat we can apply a representative-agent framework to the macro variables,despite the underlying heterogeneity in productivity, wealth, and so on. Inthis case, the joining of West Germany with another state (East Germany)that happens to have distributions of expenditure and income with lowermean values need not invalidate the representative-agent representation.The appropriate macro-level procedure is then to smoothly paste togetherin 1990–91 the initial per capita series for West Germany with that for uni-fied Germany thereafter. That is, the West German per capita growth ratesapply up to 1991, and the unified Germany growth rates apply thereafter—with no discrete shift in levels of variables at the time of the reunification.We apply this methodology to all of our cases of border change becausewe think that this approach can yield satisfactory measures of per capitagrowth rates across these changes. However, this procedure can be mis-leading with regard to levels of variables. These issues do not affect ourpresent analysis but would matter in the construction of measures of percapita C and GDP for broad groups of countries, such as the total of theOECD.
Table 2 reports means and standard deviations, by country, of annualgrowth rates of per capita C and GDP. We consider here only cases withannual data from 1914 or earlier. The sample periods end in 2006 and go
6 Brookings Papers on Economic Activity, Spring 2008
3. As an analogy, some South Koreans view a reunification with North Korea as a pend-ing disaster.
4. For example, Caselli and Ventura (2000) show that the neoclassical growth modelcan provide a satisfactory representative-agent view of macroeconomic variables despiteheterogeneity in underlying productivity and wealth.
ftn. 3
ftn. 4
TAB. 2
11302-04_Barro.qxd 8/15/08 5:38 PM Page 6
ROBERT J. BARRO and JOSÉ F. URSÚA 7
Table 2. Means and Standard Deviations of Annual Growth Rates of Consumer Expenditure and GDPa
C GDP
Standard StandardCountry Mean deviation Mean deviation
OECD countriesAustralia 0.0154 0.0506 0.0159 0.0423Austria 0.0217 0.0709Belgium 0.0189 0.0904 0.0203 0.0838Canada 0.0192 0.0474 0.0212 0.0511Denmark 0.0163 0.0538 0.0190 0.0370Finland 0.0239 0.0568 0.0237 0.0449France 0.0162 0.0674 0.0191 0.0642Germany 0.0189 0.0570 0.0212 0.0811Greeceb — — 0.0210 0.1013Iceland — — 0.0254 0.0506Italy 0.0173 0.0370 0.0213 0.0471Japan 0.0248 0.0689 0.0277 0.0611Netherlands 0.0190 0.0854 0.0188 0.0757New Zealand — — 0.0143 0.0517Norway 0.0194 0.0380 0.0231 0.0361Portugal 0.0272 0.0448 0.0207 0.0431Spain 0.0204 0.0727 0.0200 0.0453Sweden 0.0208 0.0458 0.0230 0.0362Switzerland 0.0150 0.0623 0.0150 0.0399United Kingdom 0.0147 0.0283 0.0157 0.0293United States 0.0185 0.0360 0.0217 0.0498
Non-OECD countriesArgentina 0.0189 0.0823 0.0164 0.0674Brazil 0.0277 0.0780 0.0192 0.0507Chile 0.0191 0.0905 0.0204 0.0596Colombia — — 0.0236 0.0229India — — 0.0140 0.0487Indonesia — — 0.0160 0.0556Mexico 0.0176 0.0655 0.0187 0.0421Peru 0.0174 0.0463 0.0207 0.0482South Africa — — 0.0130 0.0485South Korea 0.0293 0.0689 0.0352 0.0743Sri Lanka — — 0.0144 0.0455Taiwan 0.0344 0.0872 0.0386 0.0807Uruguay — — 0.0143 0.0787Venezuela — — 0.0251 0.0893
Source: Authors’ construction; for details on sources and procedures see the online appendix at www.economics.harvard.edu/faculty/barro/data_sets_barro.
a. C represents real per capita personal consumer expenditure; GDP represents real per capita GDP.Countries included are those with full data from before World War I, as indicated in table 1. Periods arefrom 1870 (or the later starting date with available data) through 2006. The Philippines is not included inthis table because data are missing for more than one year.
b. Value of log(GDP) in 1944 is interpolated between the values for 1943 and 1945.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 7
8 Brookings Papers on Economic Activity, Spring 2008
5. In order to have at least ten years of coverage for the 1870–1913 subperiod, table 3considers only countries with data going back at least to 1904.
Table 3. Mean Annual Growth Rates of Consumer Expenditure and GDP across Countries,Various Periodsa
C GDP
Mean of Mean of Mean of Mean of Country sample No. of growth standard No. of growth standard and period countries rates deviations countries rates deviations
OECD countries1870–1913 15 0.0141 0.0415 21 0.0141 0.03731914–47 15 0.0111 0.0871 21 0.0145 0.08851948–2006 15 0.0264 0.0257 21 0.0287 0.02841870–2006 15 0.0187 0.0538 21 0.0205 0.0544
Non-OECD countries1870–1913 6 0.0135 0.0837 11 0.0159 0.06681914–47 6 0.0147 0.0886 11 0.0132 0.07041948–2006 6 0.0264 0.0544 11 0.0257 0.04361870–2006 6 0.0225 0.0750 11 0.0198 0.0606
All countries1870–1913 21 0.0140 0.0536 32 0.0147 0.04751914–47 21 0.0121 0.0875 32 0.0140 0.08231948–2006 21 0.0264 0.0339 32 0.0276 0.03361870–2006 21 0.0196 0.0599 32 0.0202 0.0565
Source: Authors’ construction; for details on sources and procedures see the online appendix at www.economics.harvard.edu/faculty/barro/data_sets_barro.
a. C represents real per capita personal consumer expenditure; GDP represents real per capita GDP. Samplesare limited to countries from table 1 with complete data on growth rates from 1904 or earlier, so that each coun-try has at least ten observations for 1870–1913. Averages are not weighted.
back as far as possible until 1870; that is, the first observation is for thegrowth rate from 1869 to 1870.
Table 3 considers three subperiods: 1870–1913 (pre-World War I),1914–47 (which includes the two world wars and the Great Depression ofthe early 1930s), and 1948–2006 (post-World War II). The table showsaverages across the included countries of growth rates and standard devia-tions of growth rates.5 For the full period, 1870–2006, the average of thegrowth rates of C for twenty-one countries is 0.020 (that is, 2.0 percent ayear), with an average standard deviation (s.d.) of 0.060. The average forfifteen OECD countries is 0.019 (s.d. = 0.054), and that for six non-OECDcountries is 0.022 (s.d. = 0.075). For GDP, the average growth rate forthirty-two countries is 0.020 (average s.d. = 0.056). The average for twenty-one OECD countries is 0.020 (s.d. = 0.054), and that for eleven non-OECDcountries is 0.020 (s.d. = 0.061).
TAB. 3
ftn. 5
11302-04_Barro.qxd 8/15/08 5:38 PM Page 8
Table 3 shows that the last subperiod, 1948–2006, has higher growthrates and lower standard deviations than the first subperiod, 1870–1913.For example, for GDP growth in the OECD countries, the reduction in thestandard deviation—from 0.037 in 1870–1913 to 0.028 in 1948–2006—isthe kind of change found by Christina Romer for the United States andplausibly attributed mainly to improved measurement of macroeconomicaggregates.6 However, the most striking difference across the subperiodsinvolves the turbulence of the middle interval. For C growth in the OECDgroup, the average standard deviation for 1914–47 is 0.087, compared with0.042 for 1870–1913 and 0.026 for 1948–2006. Similarly, for GDP growthin the OECD group, the average standard deviation for the middle intervalis 0.088, compared with 0.037 and 0.028 in the other two periods.
An important feature of the 1870–2006 samples is that they includerealizations of disasters, notably those in the 1914–47 subperiod, whichfeatured the two world wars and the Great Depression. These realizationscreate fat tails indicated by excess kurtosis and usually lead, thereby, torejection in long samples of the hypothesis of normality for growth rates ofC or GDP.7 For C growth the only case out of twenty-one in which nor-mality is accepted (by a Jarque-Bera test) at the 5 percent level is theUnited States (p = 0.23). For GDP growth normality is accepted amongthirty-two cases only for Iceland (p = 0.07), Switzerland (p = 0.15), Brazil( p = 0.05), and Uruguay ( p = 0.51).
Appendix B presents long-term graphs of real per capita C and GDP forthe twenty-four countries that have annual data on both variables frombefore 1914. In each case the vertical axis has a natural-log scale thatranges from 5.5 to 11.0 ($245 to $59,900 in 2000 U.S. dollars). Thesegraphs bring out the long-term trends and show the major economic con-tractions. Note that a movement by 0.1 along the vertical axis correspondsto a change in the level of per capita GDP or C of about 10 percent.
As examples, for Germany GDP and C fell during World War II, WorldWar I, and the Great Depression of the 1930s. For France the dominantcontraction was during World War II, with a lesser decline in World War I.For Spain the main adverse event was its civil war during the late 1930s.The United Kingdom shows declines in C during the two world wars; GDPdid not fall during the wars, but it did during their aftermaths. In the United
ROBERT J. BARRO and JOSÉ F. URSÚA 9
6. Romer (1986).7. The tendency for negative skewness—disasters rather than bonanzas—is less pro-
nounced than we anticipated. Over the long samples, for C growth, eleven of twenty-onecountries exhibit negative skewness, and for GDP growth, twenty-four of thirty-two exhibitnegative skewness.
ftn. 6
ftn. 7
11302-04_Barro.qxd 8/15/08 5:38 PM Page 9
States the main declines in C took place during the Great Depression of theearly 1930s and in the early 1920s; GDP also fell at these times, as well asin the aftermath of World War II. An unusual case is the very strongbehavior of U.S. GDP during World War II, while C remained fairly sta-ble. The United States is also an outlier in the sense of passing the “rulertest”—a ruler placed along the pre-1914 data happens to lie along theobservations post-1950. As noted by Timothy Cogley and by Barro,8 theUnited States is almost unique in displaying this apparent tendency forthe GDP data to return to a fixed trend line. In other cases (even includingCanada, which comes close) the fixed-trend hypothesis is rejected by theGDP data. The full dataset corresponding to the appendix figures and tothe available time series for other countries is posted on the Internet.9
Rates of Return
Our study involves the interplay between macroeconomic variables, repre-sented by consumer expenditure and GDP, and rates of return on variousfinancial assets. It does not make a major contribution to the constructionof long-term data on asset returns. Instead we rely mainly on existinginformation, primarily that provided by Global Financial Data.10 Table 4shows the dates over which we have been able to assemble time series onreal rates of return. In all cases we compute arithmetic real rates of return,using consumer price indexes to deflate the nominal-return indexes. As faras possible, the return indexes and CPIs apply to the end of each year.
Table 4 considers three types of assets: stocks, short-term bills (govern-ment treasury bills with maturity of three months or less and analogousclaims such as deposits), and long-term government bonds (usually of ten-year maturity). For stocks some of the information comes from total-returnindexes, which combine price changes and dividends. In other cases weestimated returns from stock-price indexes, using rough estimates of divi-dend yields. We hope eventually to obtain data from Elroy Dimson, PaulMarsh, and Mike Staunton to extend our stock-return data backward forat least Canada, Denmark, Italy, the Netherlands, Norway, Sweden, andSwitzerland.11
Table 5 shows means and standard deviations of rates of return forcountries with nearly continuous annual time series going back at least to
10 Brookings Papers on Economic Activity, Spring 2008
8. Cogley (1990, table 2); Barro (forthcoming).9. See www.economics.harvard.edu/faculty/barro/data_sets_barro.
10. See Taylor (2005).11. Dimson, Marsh, and Staunton (2008).
ftn. 8
ftn. 9
ftn. 10, tab. 4
ftn. 11TAB. 5
11302-04_Barro.qxd 8/15/08 5:38 PM Page 10
ROBERT J. BARRO and JOSÉ F. URSÚA 11
Table 4. Starting Dates and Missing Values for Real Rates of Returna
Stocks
Total Stock Country returns indexes Bills Bonds
OECD countriesAustralia 1883 1876 1862b 1862b
Austria 1970 1923 1885b 1946[1939–44] [1938–44]
Belgium 1951 1898 [1914–18, 1849 1836b 1940, 1944–46] [1945–46] [1945–46]
Canada 1934 1916 1903 1880b
[1914–34]Denmark 1970 1915 1864 1822Finland 1962 1923 1915b 1960France 1896 1857 1841b 1841b
[1940–41] [1940–41]Germany 1870 1841 1854 1924
[1917–23]Greece 1977 1929 1915b 1993
[1941–52] [1944–45]Iceland 2003 1993 1988 1993
[2004–07] [2004–07]Italy 1925 1906 1868 1862Japan 1921 1894 1883 1871Netherlands 1951 1920 1881b 1881b
[1945–46]New Zealand 1987 1927 1923 1926Norway 1970 1915 1819 1877Portugal 1989 1932 1930b 1976
[1975–77]Spain 1941 1875 1883 1941
[1936–40]Sweden 1919 1902 1857 1922Switzerland 1967 1911 1895 1916
[1914–16]United Kingdomc 1791 1791 1801 1791United States 1801 1801 1836 1801
Non-OECD countriesArgentina 1988 1939 1978 —
[1958–66]Brazil 1988 1955 1995 —Chile 1983 1895 1864 —Colombia 1988 1928 1986 —India 1988 1921 1874 1874b
[1926–27]Indonesia 1988 1925 1970 —
[1940–77]Malaysia 1973 1974 1960 1961
(continued)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 11
12 Brookings Papers on Economic Activity, Spring 2008
12. The missing data for this group, involving two to five years each for six countries,are mainly during large wars, for which real rates of return on all three assets were probablysharply negative. This sample selection biases all measured rates of return upward, althoughthe quantitative effect cannot be too large because of the small number of years involved.The effect on computed equity premia is likely to be even smaller.
Table 4. Starting Dates and Missing Values for Real Rates of Returna (Continued)
Stocks
Total Stock Country returns indexes Bills Bonds
Mexico 1988 1930 1962 1995Peru 1993 1927 1985 —Philippines 1982 1953 1950 1997Singapore 1970 1966 1960 1988South Africa 1961 1911 1936 1896South Korea 1963 1963 1951 1957Sri Lanka 1993 1953 1951 —
[1975–84]Taiwan 1988 1968 1962 1990Turkey 1987 1987 1973 1996Uruguayd — — — —Venezuela 1988 1930e 1948 1984
Sources: Authors’ calculations using data mostly from Global Financial Data; stock-price indexes forJapan 1893–1914 are from Fujino and Akiyama (1977); bills data for Colombia, Indonesia, and Peru arefrom the International Monetary Fund. In some cases consumer price index data are from sources otherthan Global Financial Data.
a. Years in brackets are years with missing data. Rates of return are computed on an arithmetic basisusing end-of-year values of total-return indexes divided by consumer price indexes. Stock returns com-puted from stock-price indexes include rough estimates of dividend yields (or use actual dividend yieldsin some cases). Bill returns are for short-term government bills (maturity of three months or less) or, insome cases, for overnight rates, deposit rates, or central bank discount rates. Bond returns are typicallyfor ten-year government bonds but sometimes for other maturities.
b. Starting date is limited by missing consumer price index data.c. Data before 1790 are not used. Bond data are for consols up to 1932 and for ten-year government
bonds thereafter.d. Stock-price data are available starting in 1925, but estimates of dividend yields are unavailable.e. January 1942 stock-price index is used to approximate year-end value for 1941.
the 1920s.12 The first two data columns show stock and bill returns, wherea common sample applies in each case to the two types of returns. The lasttwo data columns show analogous information for bond and bill returns.We emphasize in the present study the comparison between stocks andbills—and, hence, the customary equity premium.
For the seventeen countries with matched stock and bill returns data, themean real rates of return over long-term samples were 0.0814 for stocksand 0.0085 for bills. (For each country we used a common sample forstock and bill returns.) Thus, the average equity premium was 0.0729. For
ftn. 12
11302-04_Barro.qxd 8/15/08 5:38 PM Page 12
Tab
le 5
.Lo
ng-P
erio
d Av
erag
es o
f Rat
es o
f Ret
urna
Stoc
ks-v
.-bi
lls
com
pari
son
Bon
ds-v
.-bi
lls
com
pari
son
Cou
ntry
Star
tSt
ocks
Bil
lsSt
art
Bon
dsB
ills
OE
CD
cou
ntri
esA
ustr
alia
1876
0.10
27 (
0.16
16)
0.01
26 (
0.05
66)
1870
0.03
52 (
0.11
57)
0.01
25 (
0.05
69)
Bel
gium
1870
0.02
91 (
0.15
84)b
0.01
79 (
0.14
47)b
Can
ada
1916
0.07
81 (
0.17
54)
1916
0.03
92 (
0.11
99)
Den
mar
k19
150.
0750
(0.
2300
)0.
0265
(0.
0652
)18
700.
0392
(0.
1137
)0.
0317
(0.
0588
)F
inla
nd19
230.
1268
(0.
3155
)0.
0128
(0.
0935
)—
Fra
nce
1870
0.05
43 (
0.20
78)c
−0.0
061
(0.0
996)
c18
700.
0066
(0.
1368
)−0
.007
9 (0
.100
0)G
erm
any
1870
0.07
58 (
0.29
76)
−0.0
153
(0.1
788)
1924
0.04
02 (
0.14
65)
0.01
58 (
0.11
73)
Ital
y19
060.
0510
(0.
2760
)−0
.011
2 (0
.132
8)18
700.
0173
(0.
1879
)0.
0046
(0.
1191
)Ja
pan
1894
0.09
28 (
0.30
17)
−0.0
052
(0.1
370)
1883
0.01
92 (
0.18
20)
0.00
43 (
0.14
75)
Net
herl
ands
1920
0.09
01 (
0.21
16)b
0.01
14 (
0.04
74)b
1881
0.03
08 (
0.10
67)
0.01
18 (
0.05
12)
New
Zea
land
1927
0.07
62 (
0.22
26)
0.02
34 (
0.05
29)
1926
0.02
76 (
0.12
09)
0.02
40 (
0.05
29)
Nor
way
1915
0.07
16 (
0.28
42)
0.00
98 (
0.07
82)
1877
0.02
80 (
0.11
30)
0.02
04 (
0.07
09)
Spa
in18
830.
0610
(0.
2075
)d0.
0173
(0.
0573
)d
Sw
eden
1902
0.09
23 (
0.23
47)
0.01
80 (
0.07
19)
1922
0.02
92 (
0.09
41)
0.01
76 (
0.04
48)
Sw
itze
rlan
d19
110.
0726
(0.
2107
)e0.
0083
(0.
0531
)e19
160.
0218
(0.
0717
)0.
0065
(0.
0545
)U
nite
d K
ingd
om18
700.
0641
(0.
1765
)0.
0179
(0.
0624
)18
700.
0280
(0.
1049
)0.
0179
(0.
0624
)U
nite
d S
tate
s18
700.
0827
(0.
1866
)0.
0199
(0.
0482
)18
700.
0271
(0.
0842
)0.
0199
(0.
0482
)(c
onti
nued
)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 13
Tab
le 5
.Lo
ng-P
erio
d Av
erag
es o
f Rat
es o
f Ret
urna
(Con
tinu
ed)
Stoc
ks-v
.-bi
lls
com
pari
son
Bon
ds-v
.-bi
lls
com
pari
son
Cou
ntry
Star
tSt
ocks
Bil
lsSt
art
Bon
dsB
ills
Non
-OE
CD
cou
ntri
esC
hile
1895
0.14
30 (
0.40
49)
−0.0
094
(0.1
776)
Indi
a19
210.
0514
(0.
2341
)f0.
0133
(0.
0835
)f18
740.
0191
(0.
1147
)0.
0240
(0.
0785
)S
outh
Afr
ica
1911
0.08
90 (
0.20
06)
1911
0.02
48 (
0.11
65)
Ove
rall
mea
nsg
0.08
14 (
0.24
49)
0.00
85 (
0.08
80)
0.02
66 (
0.12
34)
0.01
47 (
0.08
05)
Sour
ces:
See
tabl
e 4.
a. S
ee n
otes
to ta
ble
4. S
tand
ard
devi
atio
ns a
re in
par
enth
eses
. Col
umns
for
sto
cks
and
bills
, and
for
bon
ds a
nd b
ills,
are
for
com
mon
sam
ples
with
the
indi
cate
d st
artin
gda
te. E
nd d
ates
are
200
6.b.
Mis
sing
dat
a fo
r 19
45–4
6.c.
Mis
sing
dat
a fo
r 19
40–4
1.d.
Mis
sing
dat
a fo
r 19
36–4
0.e.
Mis
sing
dat
a fo
r 19
14–1
6.f.
Mis
sing
dat
a fo
r 19
26–2
7.g.
Ave
rage
s of
mea
ns a
nd s
tand
ard
devi
atio
ns f
or a
ll se
vent
een
coun
trie
s w
ith s
tock
and
bill
dat
a an
d al
l fift
een
coun
trie
s w
ith b
ond
and
bill
data
.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 14
the fifteen OECD countries in this sample, the average rates of returnwere 0.0793 for stocks and 0.0093 for bills, with an average equity pre-mium of 0.0699.
Since the stock returns refer to levered equity, the equity premium forunlevered equity would be smaller. For example, with a debt-equity ratioof one-half (roughly that for U.S. nonfinancial corporations in recentyears), the predicted premium for unlevered equity would be 0.0729/1.5 =0.049. Thus, we take as a challenge for the model to explain an unleveredequity premium of around 5 percent a year. This type of challenge is theone taken up long ago by Mehra and Prescott.13
The model should also be consistent with observed levels of rates ofreturn, including an average real bill rate of less than 1 percent a year.However, in the model simulations we choose the rate of time preference,ρ, to accord with the observed average level of the real bill rate (taken as arough estimate of a risk-free rate, although bills are not risk-free). The rea-soning is that the main basis for assessing a plausible value of ρ is to con-sider whether the implied levels of rates of return are sensible. Therefore,matching overall levels of rates of return does not provide a test of themodel.
For the fifteen countries (fourteen of which belong to the OECD) withmatched bond and bill returns data, the average long-term rate of return onbonds was 0.0266, compared with 0.0147 for bills over common samples.Thus, the average bond-bill premium was 0.0119. The present study doesnot address the bond-bill premium.
Table 5 also shows the familiar high annual standard deviation of stockreturns, which averaged 0.245 for the seventeen countries with matchedbill data (0.235 for the fifteen OECD countries). The corresponding aver-age standard deviation for bill returns was 0.088 (0.082 for the fifteenOECD countries). Thus, bill returns exhibited substantial volatility but notnearly as great as that of stocks.
Consumer Expenditure and GDP Disasters
To isolate economic disasters for C and GDP, we first follow the procedurein Barro’s 2006 paper by computing peak-to-trough fractional declinesthat exceed some threshold amount.14 The earlier study used a lower boundof 0.15, but we broaden this limit here to 0.10. The inclusion of contrac-
ROBERT J. BARRO and JOSÉ F. URSÚA 15
13. See Mehra and Prescott (1985).14. Barro (2006).
ftn. 13
ftn. 14
11302-04_Barro.qxd 8/15/08 5:38 PM Page 15
tions between 0.10 and 0.15 brings in many more events but has only mod-erate implications for explaining asset returns.
The peak-to-trough method for assessing the size of contractions is rea-sonable if growth rate shocks are independent and identically distributed(i.i.d.), so that level shocks are permanent. However, the method can bemisleading when some shocks to levels are temporary. Later we modifythe approach by using one-sided Hodrick-Prescott (HP) filters to attempt togauge long-run, as opposed to transitory, economic contractions. In ongo-ing research with Emi Nakamura and Jón Steinsson, we are taking a formalstatistical approach that uses the full time series for C and GDP for eachcountry. This approach considers transitional probabilities for movementsbetween normal and crisis regimes and allows for varying degrees of long-term effects of crises on levels of C and GDP.
The full results on measuring C crises are in table C1 in appendix C andare summarized in table 6. The coverage is twenty-one OECD countries(seventeen with enough data for our subsequent analysis) and fourteennon-OECD countries (seven in our later analysis). For GDP crises, shownin table C2 in appendix C and summarized in table 7, the coverage istwenty-one OECD countries (all used in our subsequent analysis) andeighteen non-OECD countries (fifteen in our later analysis). For the sam-ples used later, the mean size of C contraction (95 events for 24 countries)was 21.9 percent, and the mean size of GDP contraction (152 events for 36 countries) was 20.7 percent.
To highlight some cases, the United States has been comparativelyimmune to crises, with C declines of 16 percent in 1921 (possibly influ-enced by the influenza epidemic of 1918–20) and 21 percent during theGreat Depression in 1933. GDP declines were 10 percent in 1908 and 1914(years affected by banking panics15), 12 percent in 1921, 29 percent in1933, and 16 percent in 1947. The last contraction, likely precipitated bythe post-World War II demobilization, did not exhibit a consumptiondecline. For the United Kingdom, the two C crises were during the worldwars: 17 percent in both 1918 and 1943. There were no GDP disasters atthese times, but GDP did contract after the two wars, by 19 percent in 1921and 15 percent in 1947.
For France we found three war-related disasters for C: 16 percent in1871 (Franco-Prussian War), 22 percent in 1915 (World War I), and 58 percent in 1943 (World War II). For GDP there were six contractions,the largest measuring 41 percent in 1944. For Germany there were four C
16 Brookings Papers on Economic Activity, Spring 2008
15. See Cagan (1965, p. 138).
TAB. 6
TAB. 7
ftn. 15
11302-04_Barro.qxd 8/15/08 5:38 PM Page 16
ROBERT J. BARRO and JOSÉ F. URSÚA 17
Table 6. Summary of Consumer Expenditure Disasters by Event or Period andCountry Groupa
Average fractional
Event or period No. of decline in and country group events C per capita Declines in C per capita by country
Pre-1914OECD
Non-OECD
World War IOECD
Non-OECD
1920sOECD
Non-OECD
Great DepressionOECD
Non-OECD
Spanish civil warOECDNon-OECD
Late 1930sOECDNon-OECD
2111
10
2014
6
116
5
187
11
220101
0.160.15
0.16
0.240.26
0.18
0.180.17
0.20
0.210.19
0.22
0.290.2900.1100.11
Canada, 0.15, 0.11; Finland, 0.10;France, 0.16; Netherlands, 0.10;Spain, 0.18; Switzerland, 0.19,0.22, 0.14, 0.14, 0.16
Argentina, 0.12, 0.28, 0.20, 0.13,0.12; Brazil, 0.15, 0.16; Peru, 0.12;Taiwan, 0.22, 0.13
Australia, 0.24; Austria, 0.45;Belgium, 0.45; Canada, 0.13;Finland, 0.36; France, 0.22;Germany, 0.42; Netherlands, 0.44;Norway, 0.17; Portugal, 0.22;Spain, 0.13; Sweden, 0.12;Switzerland, 0.11; UnitedKingdom, 0.17
Argentina, 0.17; Brazil, 0.11; Chile,0.32; Malaysia, 0.10; Mexico,0.25; Singapore, 0.14
Canada, 0.20; Denmark, 0.24,Germany, 0.13; Norway, 0.16;Sweden, 0.13; United States, 0.16
Brazil, 0.15; Chile, 0.18; Malaysia,0.42; Mexico, 0.12; Singapore, 0.13
Australia, 0.23; Austria, 0.22,Canada, 0.23; Finland, 0.20;Germany, 0.12; Spain, 0.10;United States, 0.21
Argentina, 0.19; Brazil, 0.20; Chile,0.37; Colombia, 0.18; India, 0.22;Malaysia, 0.26; Mexico, 0.31;Peru, 0.14; Singapore, 0.10;Turkey, 0.12; Venezuela, 0.31
Portugal, 0.12; Spain, 0.46
Venezuela, 0.11(continued)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 17
crises: 42 percent in 1918 (World War I), 13 percent in 1923 (Germanhyperinflation), 12 percent in 1932 (Great Depression), and 41 percent in1945 (World War II). There were also four crises indicated by GDP, thelargest a remarkable 74 percent in 1946, reflecting the economic collapselate in World War II.
Many other countries suffered sharp contractions during World War II.For example, C declined in Belgium by 53 percent up to 1942, in Greeceby 64 percent up to 1944, in Japan by 64 percent up to 1945, in the Nether-lands by 55 percent up to 1944, and in Taiwan by 68 percent up to 1945.Other noteworthy cases for C were the contractions in Spain during its
18 Brookings Papers on Economic Activity, Spring 2008
World War IIOECD
Non-OECD
Post-World War IIOECD
Non-OECD
Source: Authors’ construction; for details on sources and procedures see the online appendix at www.economics.harvard.edu/faculty/barro/data_sets_barro.
a. Data for war periods include noncombatants.
Table 6. Summary of Consumer Expenditure Disasters by Event or Period andCountry Groupa (Continued)
Average fractional
Event or period No. of decline in and country group events C per capita Declines in C per capita by country
2317
6
389
29
0.240.34
0.34
0.180.14
0.19
Australia, 0.30; Austria, 0.44;Belgium, 0.53; Denmark, 0.26;Finland, 0.25; France, 0.58;Germany, 0.41; Greece, 0.64;Italy, 0.29; Japan, 64 Netherlands,0.54 Norway, 0.10; Portugal, 0.10;Spain, 0.14; Sweden, 0.18Switzerland, 0.17; UnitedKingdom, 0.17
Colombia, 0.23; India, 0.13;Malaysia, 0.34; South Korea, 0.39;Taiwan, 0.68; Turkey, 0.30
Denmark, 0.14; Finland, 0.14;Greece, 0.11; Iceland, 0.25, 0.12,0.11, 0.18; Portugal. 0.10; Spain, 0.13
Argentina, 0.10, 0.10, 0.16, 0.25;Brazil, 0.16; Chile, 0.14, 0.40,0.33; Colombia, 0.10 India, 0.18;Malaysia, 0.12, 0.14, 0.12;Mexico, 0.16, 0.11; Peru, 0.18,0.30; Singapore, 0.16, 0.12; SouthKorea, 0.37, 0.14; Turkey, 0.11;Uruguay, 0.10, 0.27, 0.22;Venezuela, 0.20, 0.22, 0.32, 0.15
11302-04_Barro.qxd 8/15/08 5:38 PM Page 18
ROBERT J. BARRO and JOSÉ F. URSÚA 19
Table 7. Summary of GDP Disasters by Event or Period and Country Groupa
Average fractional
decline Fractional decline inPeriod and No. of in GDP GDP per capitacountry group events per capita by country
Pre-1914OECD
Non-OECD
World War IOECD
Non-OECD
1920sOECD
Non-OECD
Great DepressionOECD
4519
26
2714
13
1511
4
229
0.160.15
0.17
0.210.24
0.17
0.180.16
0.22
0.220.21
Australia, 0.27; Canada, 0.12;Finland, 0.12; France (3), 0.10,0.10, 0.13; Greece (6), 0.11, 0.15,0.23, 0.15, 0.14, 0.42; Iceland,0.12; New Zealand (2), 0.17, 0.11;Spain, 0.12; Switzerland, 0.16;U.S. (2), 0.10, 0.10
Argentina (3), 0.19, 0.22, 0.15;Brazil (3), 0.10, 0.26, 0.14; Chile,0.11; India (2), 0.15, 0.10;Malaysia, 0.10; Philippines, 0.16;Singapore (2), 0.21, 0.34; SriLanka (2), 0.16, 0.14; Taiwan (2),0.21, 0.11; Uruguay (6), 0.27,0.15, 0.14, 0.20, 0.16, 0.12;Venezuela (3), 0.24, 0.22, 0.13
Australia, 0.12; Austria, 0.38;Belgium, 0.48; Denmark, 0.16;Finland, 0.35; France, 0.29;Germany, 0.36; Greece, 0.18;Iceland, 0.22; Netherlands, 0.26;New Zealand, 0.11; Norway, 0.15;Sweden, 0.15; Switzerland, 0.19
Argentina, 0.29; Chile (2), 0.10,0.13; India, 0.15; Mexico, 0.12;Philippines, 0.12; Singapore (2),0.17, 0.24; South Africa, 0.23;South Korea, 0.11; Sri Lanka, 0.14;Uruguay, 0.28; Venezuela, 0.17
Canada, 0.30; Germany, 0.14;Greece, 0.24; Iceland, 0.16; Italy,0.22; New Zealand, 0.12; Norway,0.11; Portugal, 0.11; Sweden, 0.11;U.K., 0.19; U.S., 0.12
Singapore, 0.39; South Africa, 0.24;Turkey, 0.13; Uruguay, 0.14
Australia, 0.22; Austria, 0.24;Belgium, 0.12; Canada, 0.35;France, 0.19; Germany, 0.28;Netherlands, 0.13; Spain, 0.10;U.S., 0.29
(continued)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 19
20 Brookings Papers on Economic Activity, Spring 2008
Non-OECD
Spanish civil warOECDNon-OECD
Late 1930sOECDNon-OECD
World War IIOECD
Non-OECD
Post-World War IIOECD
Non-OECD
Source: Authors’ construction; for details on sources and procedures see the online appendix at www.economics.harvard.edu/faculty/barro/data_sets_barro.
a. Data for war periods include noncombatants.
Table 7. Summary of GDP Disasters by Event or Period and Country Groupa (Continued)
Average fractional
decline Fractional decline inPeriod and No. of in GDP GDP per capitacountry group events per capita by country
13
220303
2514
11
306
24
0.23
0.230.23NA0.12NA0.12
0.360.37
0.35
0.170.13
0.17
Argentina, 0.20; Brazil, 0.20; Chile,0.36; Indonesia, 0.11; Malaysia,0.19; Mexico, 0.31; Peru, 0.26;Philippines, 0.13; Singapore, 0.41;Sri Lanka, 0.15; Turkey, 0.12;Uruguay, 0.37; Venezuela, 0.16
Portugal, 0.15; Spain, 0.31
Malaysia, 0.12; Singapore, 0.15;South Korea, 0.10
Australia, 0.14; Austria, 0.59;Belgium, 0.45; Denmark, 0.24;Finland, 0.10; France, 0.41;Germany, 0.74; Greece, 0.66;Italy, 0.41; Japan, 0.50;Netherlands, 0.52; Norway, 0.19;Sweden, 0.10; Switzerland, 0.13
India, 0.12; Indonesia, 0.54;Malaysia (2), 0.24, 0.36;Philippines, 0.57; South Korea,0.48; Sri Lanka, 0.21; Taiwan,0.66; Turkey, 0.40; Uruguay, 0.14;Venezuela, 0.16
Finland, 0.12; Iceland, 0.14; NewZealand (2), 0.12, 0.10; U.K.,0.15; U.S., 0.16
Argentina (4), 0.10, 0.11, 0.14, 0.22;Brazil, 0.11; Chile (2), 0.24, 0.18;Indonesia, 0.16; Mexico, 0.13;Peru (3), 0.10, 0.14, 0.32;Philippines, 0.19; Singapore (2),0.34, 0.11; South Africa (2), 0.11,0.10; South Korea, 0.15; Uruguay(3), 0.12, 0.24, 0.19; Venezuela(3), 0.15, 0.30, 0.26
11302-04_Barro.qxd 8/15/08 5:38 PM Page 20
civil war, by 46 percent up to 1937, and in Chile during the 1970s militarytakeover period, by 40 percent up to 1976.
U.S. studies often focus on the severity of the Great Depression; in fact,some researchers gauge disaster probabilities entirely from this singleevent.16 One reason for this focus on the Depression is that the UnitedStates happened to do well economically during the two world wars, whichwere major economic disasters for much of the rest of the world, includingmany OECD countries. However, even if one’s concern is limited to fore-casting U.S. disasters or studying disaster probabilities as perceived byinvestors in the United States, it seems plausible that the global experience—particularly of comparable OECD countries—would provide a great dealof information. Our perspective is that U.S. prospects can be gauged muchbetter by consulting the global experience, rather than overweighting theUnited States’ own history for which the few observed disasters are likelyto be dominated by luck.
In a global context, at least since 1870, the most serious economic dis-aster in terms of incidence and severity of declines in C and GDP wasWorld War II. This event was followed in terms of economic impact byWorld War I and the Great Depression of the early 1930s—two eventswith similar overall consequences.
Among the thirty-five countries included for C in appendix table C1,table 6 shows that World War II had twenty-three crises with an averagesize of 34 percent. (This table includes noncombatant experiences as partof the war periods.) World War I had twenty crises with an average size of24 percent, and the Great Depression had eighteen crises with an averagesize of 21 percent. The 1920s had another eleven events, including eightwith troughs in 1920–21, with an average size of 18 percent. As alreadymentioned, the contractions at the start of the 1920s may reflect theinfluenza epidemic of 1918–20.17 We also found twenty-one pre-1914events (for a truncated sample because of missing data) with an averagesize of 16 percent.
The post-World War II period was remarkably calm for the OECDcountries: only nine consumption crises were found, four of which were inIceland (relating in part to shocks to the fishing industry). The largest crisisoutside of Iceland was 14 percent for Finland in the early 1990s (a crisisthought to originate from the changed economic relationship with the for-mer Soviet Union). However, economic crises have not disappeared from
ROBERT J. BARRO and JOSÉ F. URSÚA 21
16. See, for example, Chatterjee and Corbae (2007) and Cogley and Sargent (forth-coming).
17. Ursúa (2008).
ftn. 16
ftn. 17
11302-04_Barro.qxd 8/15/08 5:38 PM Page 21
the world, as is clear from the twenty-nine non-OECD consumption eventswith an average size of 19 percent. The disasters here include the LatinAmerican debt crisis of the early 1980s, the Asian financial crisis of thelate 1990s, and the difficulties in 2001–02 in Argentina related to the col-lapse of that country’s currency board.
Table 7 provides a roughly similar picture for crises gauged by percapita GDP. For the thirty-nine countries included in appendix table C2,World War II had twenty-five events with an average size of 36 percent.World War I had twenty-seven events with a mean size of 21 percent, andthe Great Depression had twenty-two cases with an average size of 22 per-cent. The 1920s had another fifteen events—ten of them with troughs in1920–21—with a mean size of 18 percent. The pre-1914 period (moreplentiful than for consumer expenditure) showed forty-five events, with anaverage size of 16 percent. The post-World War II period featured only sixevents for the OECD; the largest were the post-World War II aftermathsfor the United States (16 percent) and the United Kingdom (15 percent).Again, the situation was much less calm outside of the OECD: twenty-fourevents with an average size of 17 percent.
Consumer Durables
The consumption concept that enters into asset pricing equations would becloser to real consumer expenditure on nondurable goods and services(subsequently referred to as nondurables) than to overall consumer expen-diture. That is, one might want to exclude durables outlays or, better yet,include an estimate of rental income on the slowly moving stock ofdurables. However, except for the OECD countries after World War II(which had few crises), we typically lack the data to divide personal con-sumer expenditure into durables and nondurables expenditure.
Table C3 in appendix C shows the twenty-eight cases among the Cdisasters from table C1 for which we have been able to locate data that per-mit a breakdown in the decline in real personal consumer expenditure intodurables and nondurables. Twenty of these cases are in our main sampleof ninety-five C crises. Not surprisingly, the proportionate decreases indurables expenditure were typically much larger than those in non-durables. On average for the twenty-eight crises, the proportionate fall inper capita C was 18.3 percent, that in durables was 39.6 percent, and that innondurables was 15.1 percent. Thus, a substitution of nondurables expen-diture for overall consumer expenditure would reduce the mean size ofcontraction among the twenty-eight cases by about 3 percentage points.
22 Brookings Papers on Economic Activity, Spring 2008
11302-04_Barro.qxd 8/15/08 5:38 PM Page 22
The main reason that the adjustment for durables has only a moderate,though significant, impact is that the share of nominal durables expendi-ture in total personal consumer expenditure is usually not large, averaging8.0 percent at the peaks and 5.8 percent at the troughs for the twenty-eightcases considered in table C3.18 As an extreme example, for the UnitedKingdom during World War II, the measured durables share fell to only2.3 percent in 1943 (with household spending on automobiles falling tonear zero). But since the durables share of nominal personal consumerexpenditure at the peak in 1938 was only 4.9 percent, the adjustment wasstill only 2.5 percentage points; that is, the proportionate fall in non-durables was 14.4 percent, compared with 16.9 percent for all personalconsumer expenditure.
The average durables adjustment of 3 percentage points likely over-states the overall effects. The reason is that we are systematically missingdata on the breakdown between durables and nondurables for the largercrises: the mean contraction in C for the twenty-eight cases in table C3 was18.3 percent, compared with a mean of 21.9 percent for the ninety-five Ccontractions used in our subsequent analysis. The largest C contractions intable C3 are 46 percent for Spain in 1937, 36 percent for Finland in 1918,33 percent for Chile in 1985, and 32 percent for Venezuela in 1989.
Consider an arithmetic formula for the magnitude of the proportionatechange in nondurables—this formula applies when durables and non-durables are both declining, with the size of the fractional decline indurables exceeding that in nondurables:
where C is total consumer expenditure, D is durables expenditure, and NDis nondurables expenditure. We have already noted that the size of theadjustment is limited by the modest share of durables in total expenditure—this effect comes through the term D/ND.
An additional effect in equation 1 is that as we consider contractionswith larger magnitude for ΔC/C, the difference between the size of ΔD/Dand that of ΔC/C must, at least eventually, get smaller. For example, thelargest possible magnitude of ΔD/D is one. In this extreme situation, theamount of adjustment in switching to nondurables has to fall as the size ofΔC/C gets larger (with the adjustment approaching zero as the size of
( ) ,1Δ Δ Δ ΔND
ND
C
C
D
ND
D
D
C
C= − ⎛
⎝⎜⎞⎠⎟
−⎡⎣⎢
⎤⎦⎥
i
ROBERT J. BARRO and JOSÉ F. URSÚA 23
18. The change in the nominal share of durables from peak to trough depends partly onthe relative growth rates of real durables versus nondurables and partly on the relativegrowth rates of prices of durables versus nondurables.
ftn. 18
11302-04_Barro.qxd 8/15/08 5:38 PM Page 23
ΔC/C approaches one). This reasoning suggests that the durables adjust-ment would tend to be less important (in percentage points) for the largercrises—and these are the ones that matter most for replicating the equitypremium in our later analysis. We do see this pattern in appendix table C3:for Spain in 1937 the adjustment is from 46.1 percent to 45.0 percent; forFinland in 1918 the adjustment is from 36.0 percent to 35.3 percent; andfor Venezuela in 1989 the adjustment is from 32.0 percent to 29.9 percent.However, for Chile in 1985 the adjustment is much larger, from 32.7 per-cent to 17.9 percent.
In any event, we lack information in most cases on the breakdown ofpersonal consumer expenditure into durables and nondurables. Althoughwe may add a few cases, we will not be able to go much beyond the cover-age shown in appendix table C3. Therefore, we apply the rest of our analy-sis to crises gauged by personal consumer expenditure, C, in appendixtable C1, as well as to crises measured by GDP in appendix table C2.
Consumer Expenditure and GDP Disasters Compared
Table 8 matches C and GDP disasters for countries with full data (seven-teen OECD and seven non-OECD). We match the C and GDP contractionsin appendix tables C1 and C2, respectively, by trough years—either thesame or a nearby year. In some cases a contraction by 0.10 or more in C orGDP does not pair up with a decline of at least 0.10 in the other variable (inwhich case the decline in the other variable does not appear in appendixtable C1 or C2). In those cases we enter in table 8 the actual decline in theother variable (where, for a few cases, a negative value means that the vari-able increased).
Macroeconomists, particularly those familiar with U.S. data, tend tobelieve that proportionate contractions in consumer expenditure duringrecessions are typically smaller than those in GDP. Partly this view comesfrom the Great Depression, and the numbers in appendix tables C1 and C2bear out this perspective: as an example, the proportionate declines in theUnited States up to 1933 were 21 percent for C and 29 percent for GDP.The idea that C is relatively more stable than GDP reflects also the generalpatterns in post-World War II macroeconomic fluctuations, includingthose in the United States. Since 1954, the standard deviation of the cyclicalpart of U.S. real GDP was 1.6 percent, compared with 1.2 percent for realconsumer expenditure.19 The main counterpart of the smoother behavior
24 Brookings Papers on Economic Activity, Spring 2008
19. Barro (2008, p. 185).
TAB. 8
ftn. 19
11302-04_Barro.qxd 8/15/08 5:38 PM Page 24
Tab
le 8
.M
atch
ed C
onsu
mer
Exp
endi
ture
and
GD
P Co
ntra
ctio
nsa
OE
CD
cou
ntri
esN
on-O
EC
D c
ount
ries
C p
er c
apit
aG
DP
per
cap
ita
C p
er c
apit
aG
DP
per
cap
ita
Tro
ugh
Size
of
Tro
ugh
Size
of
Tro
ugh
Size
of
Tro
ugh
Size
of
Cou
ntry
year
cont
ract
ion
year
cont
ract
ion
Cou
ntry
year
cont
ract
ion
year
cont
ract
ion
Aus
tral
ia19
180.
238
1918
0.11
8A
rgen
tina
1891
0.12
318
910.
189
1932
0.23
419
310.
221
1898
0.28
318
970.
219
1944
0.30
119
460.
145
1900
0.19
519
000.
147
Bel
gium
1917
0.44
519
180.
477
1902
0.12
719
020.
049
1934
0.09
219
340.
117
1907
0.12
319
070.
025
1942
0.53
019
430.
453
1917
0.17
219
170.
289
Can
ada
1876
0.15
218
780.
117
1932
0.18
919
320.
195
1908
0.11
319
080.
078
1959
0.10
119
590.
101
1915
0.13
019
140.
095
1982
0.10
419
820.
111
1921
0.19
619
210.
301
1990
0.16
019
900.
141
1933
0.23
019
330.
348
2002
0.24
920
020.
220
Den
mar
k19
170.
074
1918
0.16
0B
razi
l19
050.
148
1904
0.04
019
210.
241
1921
0.04
219
090.
157
1908
0.06
119
410.
261
1941
0.23
919
190.
109
1918
0.04
419
480.
144
1945
0.08
719
210.
147
1921
0.00
2F
inla
nd18
920.
102
1892
0.07
519
310.
201
1931
0.20
119
180.
360
1918
0.35
319
900.
163
1992
0.11
019
320.
199
1932
0.06
2C
hile
1903
0.04
819
030.
111
1944
0.25
419
400.
103
1915
0.32
219
150.
105
1993
0.14
019
930.
124
1922
0.18
119
190.
126
Fra
nce
1871
0.15
818
700.
095
1932
0.37
419
320.
361
1878
0.08
518
790.
102
1956
0.13
619
560.
038
1884
0.08
518
860.
133
1976
0.40
119
750.
240
1915
0.21
519
180.
289
1985
0.32
719
830.
180
(con
tinu
ed)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 25
1936
0.06
219
350.
187
Mex
ico
1916
0.25
219
150.
119
1943
0.58
019
440.
414
1924
0.11
819
240.
032
Ger
man
y19
180.
425
1919
0.35
719
320.
311
1932
0.25
819
230.
127
1923
0.13
519
880.
161
1988
0.12
819
320.
121
1932
0.28
019
950.
113
1995
0.08
019
450.
412
1946
0.73
6P
eru
1914
0.11
819
140.
019
Ital
y19
190.
026
1920
0.22
119
320.
140
1932
0.25
819
450.
286
1945
0.41
319
790.
179
1979
0.10
4Ja
pan
1945
0.63
919
440.
503
1983
0.07
519
830.
136
Net
herl
ands
1893
0.09
818
930.
062
1992
0.30
019
920.
325
1918
0.44
019
180.
258
S. K
orea
1920
0.06
619
190.
111
1935
0.04
519
340.
129
1939
0.06
819
390.
104
1944
0.54
519
440.
525
1945
0.38
719
450.
480
Nor
way
1918
0.16
919
180.
148
1952
0.37
119
510.
151
1921
0.16
119
210.
110
1998
0.14
319
980.
078
1944
0.10
019
440.
193
Tai
wan
1905
0.21
919
050.
214
Por
tuga
l19
190.
215
1918
0.08
619
110.
127
1911
0.11
419
280.
062
1928
0.10
919
450.
684
1945
0.66
219
360.
121
1936
0.14
819
420.
104
1945
0.04
819
760.
098
1975
0.08
5
Tab
le 8
.M
atch
ed C
onsu
mer
Exp
endi
ture
and
GD
P Co
ntra
ctio
nsa
(Con
tinu
ed)
OE
CD
cou
ntri
esN
on-O
EC
D c
ount
ries
C p
er c
apit
aG
DP
per
cap
ita
C p
er c
apit
aG
DP
per
cap
ita
Tro
ugh
Size
of
Tro
ugh
Size
of
Tro
ugh
Size
of
Tro
ugh
Size
of
Cou
ntry
year
cont
ract
ion
year
cont
ract
ion
Cou
ntry
year
cont
ract
ion
year
cont
ract
ion
11302-04_Barro.qxd 8/15/08 5:38 PM Page 26
Spa
in18
960.
182
1896
0.11
919
150.
128
1918
0.03
819
300.
101
1933
0.09
619
370.
461
1938
0.31
319
450.
145
1945
0.08
419
490.
131
1949
0.01
3S
wed
en19
170.
115
1918
0.15
019
210.
132
1921
0.10
819
450.
182
1941
0.09
5S
wit
zerl
and
1872
0.19
018
700.
052
1878
0.22
518
790.
161
1883
0.14
218
830.
065
1886
0.14
118
870.
003
1888
0.15
718
870.
003
1918
0.10
819
180.
191
1945
0.17
319
420.
126
Uni
ted
1918
0.16
719
18−0
.022
Kin
gdom
1921
0.00
519
210.
192
1943
0.16
919
43−0
.014
1948
0.00
119
470.
148
Uni
ted
1908
0.03
719
080.
105
Sta
tes
1915
0.04
619
140.
095
1921
0.16
419
210.
118
1933
0.20
819
330.
290
1947
0.00
119
470.
165
Sour
ce: A
utho
rs’
cons
truc
tion;
for
det
ails
on
sour
ces
and
proc
edur
es s
ee th
e on
line
appe
ndix
at w
ww
.eco
nom
ics.
harv
ard.
edu/
facu
lty/b
arro
/dat
a_se
ts_b
arro
.a.
Thi
s ta
ble
only
incl
udes
the
seve
ntee
n O
EC
D c
ount
ries
and
the
seve
n no
n-O
EC
D c
ount
ries
that
are
in o
ur f
ull s
ampl
es f
or p
erso
nal c
onsu
mer
exp
endi
ture
, C, a
nd G
DP.
Con
-tr
actio
ns o
f 0.
10 o
r m
ore
com
e fr
om ta
bles
C1
and
C2
(with
add
ition
s fr
om u
nder
lyin
g da
ta f
or c
ases
whe
re C
or
GD
P co
ntra
ctio
ns w
ere
of m
agni
tude
less
than
0.1
0). C
ontr
actio
nsar
e m
atch
ed b
y tr
ough
yea
rs (
the
sam
e or
nea
rby)
. Ita
lics
for
trou
gh y
ear
indi
cate
par
ticip
atio
n as
war
com
bata
nt.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 27
of C than of GDP was the sharply fluctuating investment. That is, the steepdeclines in investment during U.S. recessions, including the Great Depres-sion, partly buffered the decreases in consumer expenditure.20 This buffer-ing could also apply, in principle, to the current account balance; that is, aprocyclical current account would moderate fluctuations in consumerspending (and investment) relative to those in GDP. However, in the post-1954 period, the ratio of the U.S. current account balance to GDP wasactually weakly countercyclical.21
From a theoretical standpoint (and despite the validity of the permanent-income hypothesis), it is not inevitable that consumption would fluctuateproportionately by less than GDP. These patterns depend on whether theunderlying macroeconomic shocks impinge more on investment demandor on desired saving. This balance depends, in turn, on the permanenceof the shocks and whether they operate primarily as income effects or asshifts to the productivity of capital. In a simple AK model with i.i.d.shocks to the growth rate of productivity, A, consumption and GDP wouldalways have the same proportionate variations.
An important consideration during wartime is the sharp increase in gov-ernment purchases for the military. This expansion of government spend-ing decreases C (and investment) for a given GDP.22 In our data many ofthe C and GDP crises—and a disproportionate share of the larger crises—feature these wartime expansions of government spending. In such circum-stances C would tend to decline proportionately by more than GDP.
Table 9, based on the matching of contractions shown in table 8, covers112 contractions overall, 70 for OECD countries and 42 for non-OECDcountries. Of the 112 contractions, 31 featured participation of the countryas a war combatant and 81 were nonwar (where the label “nonwar” includesnoncombatants during major wars). In the eighty-one nonwar cases, theaverage proportionate decrease in C was slightly greater than that in GDP:14.6 percent versus 12.9 percent (12.6 percent versus 12.4 percent for theOECD countries). In the thirty-one war cases, the margin was greater:31.8 percent versus 27.2 percent (32.0 percent versus 27.6 percent for theOECD countries).
28 Brookings Papers on Economic Activity, Spring 2008
20. This pattern is stronger for consumption measured by expenditure on nondurablesand services, that is, when expenditures on consumer durables are grouped with investment.
21. Barro (2008, p. 429).22. The declines in consumption and investment could be moderated by falls in the cur-
rent account balance. However, the option of borrowing from abroad tends to be severelylimited during a global conflict. Moreover, even in localized conflicts, combatants are likelyto be cut off from international borrowing.
ftn. 20
ftn. 21
ftn. 22
TAB. 9
11302-04_Barro.qxd 8/15/08 5:38 PM Page 28
In terms of timing patterns, table 9 shows for the full sample of 112crises that 66 have the same trough years for C and GDP. The trough yearfor C comes later in twenty-six cases, whereas that for GDP comes later intwenty cases. Thus, at least in the annual data, there is no clear pattern as towhether C or GDP reaches its trough first during crises. If we consider onlywartime cases, fifteen of the thirty-one have the same trough year, whereasC reaches its trough later in seven and GDP reaches its trough later in nine.Thus, there is also no clear result on the timing pattern during wars.
One concern is that the apparent excess of the average size of C con-tractions over GDP contractions might reflect greater measurement error inthe C data. In future formal statistical analysis of the C and GDP timeseries, we will allow for measurement error that might differ across coun-tries, over time, and between the C and GDP data. For now we can getsome idea about the role of measurement error by redoing the analysisusing trend values of log(C) and log(GDP) calculated from HP filters. Weuse a conventional smoothing parameter for annual data of 100. Unlike inthe standard setup, we use one-sided filters; that is, we consider only cur-rent and past values at each point in time when estimating “trends.” (Thisprocedure avoids the implication that people knew in advance of a comingdestructive war or depression, so that they knew that a major decline in
ROBERT J. BARRO and JOSÉ F. URSÚA 29
Table 9. Means and Relative Timing of Matched Consumer Expenditure and GDP Contractionsa
Trough of C contraction occurred
Mean C Mean GDP In same year as Before GDP After GDP contraction contraction GDP contraction contraction contraction
OECD countriesAll (70 contractions) 0.190 0.174 35 19 16Wartime (23) 0.320 0.276 10 9 4Non-wartime (47) 0.126 0.124 25 10 12
Non-OECD countriesAll (42 contractions) 0.199 0.159 31 1 10Wartime (8) 0.311 0.260 5 0 3Non-wartime (34) 0.173 0.135 26 1 7
Full sampleAll (112 contractions) 0.194 0.168 66 20 26Wartime (31) 0.318 0.272 15 9 7Non-wartime (81) 0.146 0.129 51 11 19
Source: Authors’ construction; for details on sources and procedures see the online appendix at www.economics.harvard.edu/faculty/barro/data_sets_barro.
a. Means and timing are for the matched contractions listed in table 8.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 29
trend C or GDP was about to happen.) Instead of computing proportionatepeak-to-trough decreases in C or GDP during crises, we calculate here theproportionate peak-to-trough decreases in the HP trend values. This proce-dure downplays short-lived contractions and tends to count only the morepersistent declines. It also tends to filter out downturns that are merely aresponse to a previous upward blip in C or GDP. Most important in thepresent context, the HP filter tends to eliminate “crises” that reflect mainlytemporary measurement error in C and GDP.
The HP filtering procedure substantially reduces the estimated numberof disasters, from 95 to 43 for C and from 152 to 70 for GDP. The fullresults are presented in tables C4 and C5 in appendix C. We matched the Cand GDP crises, as before, and found thirty nonwar pairs (seventeen inOECD countries and thirteen in non-OECD countries) and twenty-threewartime pairs (nineteen in OECD countries and four in non-OECD coun-tries). In the nonwar sample, the average size of C decline was 12.0 per-cent, compared with 14.0 percent for GDP (8.8 percent and 13.4 percent,respectively, for the OECD countries). In the war sample, the mean sizeof C decline was 28.9 percent, compared with 23.8 percent for GDP(27.4 percent and 21.7 percent, respectively, for the OECD countries).Thus, the HP-filtered data generate wartime patterns that are similar tothose found before: the average magnitude of C decline was larger thanthat for GDP. However, the findings for nonwar samples are reversed, withthe average size of C decline smaller than that for GDP. Thus, overall, themain robust finding is that C tends to fall proportionately more than GDPduring wartime crises. The relative magnitude of decline during nonwarcrises is less clear.
Disaster Probability and the Frequency Distribution of Disaster Sizes
This section considers the sample of countries with essentially completeannual time series since before 1914. We use twenty-four countries(including seventeen OECD countries) on per capita consumer expendi-ture, C, and thirty-six countries (including twenty-one OECD countries)on per capita GDP.23 For the C sample of twenty-four countries, we iso-lated ninety-five disasters (appendix table C1). The upper panel of figure 1
30 Brookings Papers on Economic Activity, Spring 2008
23. We include Greece and the Philippines in the GDP sample. Although GDP data aremissing for Greece in 1944 and for the Philippines in 1941–45, we can compute the peak-to-trough GDP declines during World War II in each case: 66 percent for Greece from 1939 to1942 and 57 percent for the Philippines from 1939 to 1946.
ftn. 23FIG. 1
11302-04_Barro.qxd 8/15/08 5:38 PM Page 30
ROBERT J. BARRO and JOSÉ F. URSÚA 31
Figure 1. Distributions of Consumer Expenditure Disasters by Size and Durationa
Source: Authors’ construction; for details on sources and procedures see the online appendix at www.economics.harvard.edu/faculty/barro/data_sets_barro.
a. The sample is our main sample of ninety-five personal consumption expenditure disasters from appendix table C1.
4
12
16
No. of eventsBy size
N = 95, mean = 0.219
Cumulative fractional decline in real personal consumer expenditure per capita
8
0.2 0.3 0.4 0.5 0.6 0.7
4
12
16
No. of eventsBy duration
N = 95, mean = 3.6
Duration (years between trough and peak)
8
21 3 4 5 6 7 8 9
11302-04_Barro.qxd 8/15/08 5:38 PM Page 31
plots the frequency distribution of these C declines. The bottom panelshows the frequency distribution of the duration of these disasters (gauged,in each case, by the number of years from “peak” to “trough”). The aver-age size was 22 percent, and the average duration was 3.6 years. For theGDP sample of thirty-six countries, we found 152 disasters (appendixtable C2). The upper panel of figure 2 plots the frequency distribution ofthese GDP declines, and the bottom panel shows the frequency distributionof the disaster durations. The average size was 21 percent, and the averageduration was 3.5 years. Appendix figures D1 and D2 show the frequencydistribution graphs for C and GDP corresponding to the HP-filtered data.The mean disaster sizes are very similar to the nonfiltered cases (23 per-cent for GDP and 22 percent for C), but average durations are longerbecause of the smoothing procedure (6.3 years for GDP and 6.4 yearsfor C).
In our subsequent simulation of a model of the equity premium, usingthe disaster data to calibrate the model, the results depend mainly on theprobability of disaster, p, and the frequency distribution of the proportion-ate disaster size, b. With substantial risk aversion, the key aspect of thesize distribution is not so much the mean of b but, rather, the fatness of thetails; that is, the likelihood of extremely large disasters.
Suppose that there are two states, normalcy and disaster. With probabil-ity p per year (taken here to be constant over time and across countries),the economy shifts from normalcy to disaster. With another probability πper year (also constant over time and across countries), the economy shiftsfrom disaster to normalcy. As mentioned before, we found 95 disasters forC and 152 for GDP. Also as noted before, we measured disaster-years bythe interval between peak and trough for each event. This calculationyields 343 disaster-years for C and 530 disaster-years for GDP. The totalnumber of annual observations is 2,963 for C and 4,653 for GDP. There-fore, the number of normalcy years is 2,620 for C and 4,123 for GDP. Weestimate p as the ratio of the number of disasters to the number of normalyears. This calculation yields p = 0.0363 for C and 0.0369 for GDP.24 Weestimate π as the ratio of the number of disasters (all of which eventuallyended) to the number of disaster-years. This computation gives π = 0.277for C and 0.287 for GDP. Therefore, whether we gauge by C or by GDP,we can think of disasters as starting with a probability of around 3.6 per-cent a year and ending with a probability of about 28 percent a year.
32 Brookings Papers on Economic Activity, Spring 2008
24. The main reason that these disaster probabilities exceed those in Barro (2006) is theinclusion of disaster sizes between 0.10 and 0.15. If we consider only disasters of 0.15 orgreater, the probabilities are p = 0.0218 for C and 0.0192 for GDP.
FIG. 2
ftn. 24
11302-04_Barro.qxd 8/15/08 5:38 PM Page 32
ROBERT J. BARRO and JOSÉ F. URSÚA 33
Figure 2. Distributions of GDP Disasters by Size and Durationa
Source: Authors’ construction; for details on sources and procedures see the online appendix atwww.economics.harvard.edu/faculty/barro/data_sets_barro.
a. The sample is our main sample of 152 GDP disasters from appendix table C2.
4
12
16
No. of eventsBy size
N = 152, mean = 0.207
Cumulative fractional decline in real GDP per capita
8
0.2 0.3 0.4 0.5 0.6 0.7
4
12
16
No. of eventsBy duration
N = 152, mean = 3.5
Duration (years between trough and peak)
8
21 3 4 5 6 7 8 9 10
11302-04_Barro.qxd 8/15/08 5:38 PM Page 33
The frequency distributions for disaster size, b, shown for C and GDP,respectively, in the upper panels of figures 1 and 2, turn out to be wellapproximated by Pareto or power-law forms. These representations havebeen found to apply to an array of economic and physical phenomena,including amounts of stock-price changes and sizes of cities and firms.25
We plan to work out the application of power-law distributions to disastersizes in future research.
A Lucas-Tree Model of Rates of Return
The estimates of p and the b distribution can be matched with rates ofreturn determined in a representative-agent Lucas-tree setting.26 Our theo-retical framework, summarized briefly here, follows that in a forthcomingpaper by Barro, which extends his 2006 paper to use the Epstein-Zin-Weil(EZW) form of consumer preferences.27 That is, we allow for two distinctpreference parameters: γ, the coefficient of relative risk aversion, and θ,the reciprocal of the intertemporal elasticity of substitution (IES).
We set up the model, for convenience, in terms of discrete periods.However, the formulas derived later apply as the length of the periodapproaches zero. The log of real GDP evolves exogenously as a randomwalk with drift:
The first random term, ut+1, is i.i.d. normal with mean zero and variance σ2.This term reflects “normal” economic fluctuations due, for example, toproductivity shocks. The parameter g ≥ 0 is a constant that reflects exoge-nous productivity growth. Population is constant, so Yt represents percapita GDP as well as the level of GDP.
The second random term, vt+1, picks up rare disasters, as in Rietz’s ear-lier work and Barro’s 2006 paper.28 In these rare events, output and con-sumption jump down sharply. The probability of a disaster is the constantp ≥ 0 per unit of time. In a disaster, output and consumption contract by thefraction b, where 0 < b < 1. The distribution of vt+1 is given by
( ) log log .2 1 1 1Y Y g u vt t t t+ + +( ) = ( ) + + +
34 Brookings Papers on Economic Activity, Spring 2008
25. See Mandelbrot (1963), Fama (1965), and Gabaix (1999).26. Lucas (1978).27. Epstein and Zin (1989); Weil (1990).28. Rietz (1988); Barro (2006).
ftn. 25
ftn. 26
ftn. 27
ftn. 28
11302-04_Barro.qxd 8/15/08 5:38 PM Page 34
The disaster size, b, follows some probability distribution, which we gaugeby the empirical densities shown in figures 1 and 2.
In the baseline Lucas-tree setting—a closed economy with no invest-ment and no government purchases—the representative agent’s consump-tion, Ct, equals output, Yt.29 Given the processes that generate ut+1 and vt+1,the expected growth rate of Ct and Yt, denoted by g*, is given by
where E(b) is the expected value of b. (Note that we have allowed for dis-asters but not for “bonanzas.”)
A key simplification, which allows for closed-form solutions, is that theshocks ut+1 and vt+1 in equation 2 are i.i.d.; that is, they represent permanenteffects on the level of output, rather than transitory disturbances to the level.An important part of our ongoing research is to reassess this i.i.d. assump-tion, in particular, to allow for transitory effects from disasters, such aswars and financial crises. (Another important extension, needed to matchthe observed volatility of stock prices and rates of return, is to allow fortime variation in the uncertainty parameters, particularly the disaster prob-ability, p.)
In general, EZW preferences do not yield closed-form solutions forasset pricing equations. However, Barro shows that with i.i.d. shocks (as inthe present model), the first-order optimizing conditions generate assetpricing equations of familiar form:30
where Rt is the one-period gross return on any asset. This specification dif-fers from the standard power-utility model (γ = θ) in that, first, the exponenton consumption is the negative of the coefficient of relative risk aversion,
( )*
,41
11C E R Ct t t t
−+−=
+
⎛
⎝⎜
⎞
⎠⎟ ( )γ γ
ρi i
( ) * ,3 1 2 2g g p E b= + ( ) − ( )σ i
probabilityprobability
1 01
1
− ==
+
+
p vp v
t
t
:: logg .1 −( )b
ROBERT J. BARRO and JOSÉ F. URSÚA 35
29. We can readily incorporate wartime related government purchases, Gt, which do notsubstitute for Ct in household utility but do create a wedge between Yt and Ct. In this case anincrease in Gt amounts to a decrease in productivity. Results on asset returns are similar in anAK model with endogenous investment and stochastic (i.i.d.) depreciation shocks; see Barro(forthcoming). In this setting, a disaster amounts to a large-scale destruction of Lucas trees.
30. Barro (forthcoming).
ftn. 29
ftn. 30
11302-04_Barro.qxd 8/15/08 5:38 PM Page 35
γ (not θ), and second, the effective rate of time preference, ρ*, differs fromthe usual rate of time preference, ρ, when γ ≠ θ. The formula for ρ* is
where E is the expectations operator and g* is the expected growth rategiven in equation 3.
The formulas for the expected rate of return on equity (unlevered claimsto Lucas trees), r e, and the risk-free rate, r f, can be derived from equation4, given the process that generates Yt and Ct in equation 2. The results are
Hence, the equity premium can be expressed as
which depends only on γ and the uncertainty parameters (σ, p, and the dis-tribution of b). The first term, γσ2, is negligible and corresponds to the no-disaster equity premium of Mehra and Prescott.31 The second term bringsin disasters and is proportional to the disaster probability, p. The disastersize, b, enters as the expectation of the product of b (the proportionatedecline in consumption) and the proportionate excess of the “marginal util-ity of consumption”32 in a disaster state, [(1 − b)−γ − 1]. This second termtends to be large.
The formulas for rates of return and the equity premium in equations 6through 8 depend on a number of assumptions. The baseline model assumesthat property rights in assets are perfectly maintained; in particular, there
( ) ,8 1 12r r p E b be f− = + −( ) −⎡⎣ ⎤⎦{ }−γσ γi i
( ) * *7 1 2 1
1 1
2r g
p E b
f = + − ( ) +( )− −( ) − −−
ρ γ γ γ σ
γγ
i i i
i ii E b( )⎡⎣ ⎤⎦.
( ) * *6 1 2 1
1 1
2
1
r g
p E b
e = + − ( ) −( )− −( ) − −−
ρ γ γ γ σγ
i i i
i γγ −( ) ( )⎡⎣ ⎤⎦1 i E b
( ) * *5 1 21
1
2ρ ρ γ θ γσγ
= −( )⎧⎨⎪
⎩⎪− ( ) −
−⎛⎝⎜
⎞⎠⎟
i i
i
gp
E −−( ) − − −( ) ( )⎡⎣ ⎤⎦
⎫⎬⎪
⎭⎪
−b E b
11 1
γ γ i ,
36 Brookings Papers on Economic Activity, Spring 2008
31. Mehra and Prescott (1985).32. This interpretation would be precise for power utility (γ = θ).
ftn. 32
ftn. 31
11302-04_Barro.qxd 8/15/08 5:38 PM Page 36
are no possibilities for default on stocks or risk-free claims. The analysiscan be extended to allow for partial defaults during crises.33 Aside fromformal repudiation of claims, default can involve erosion of the real valueof nominal claims through surprise jumps in the price level. This type ofdefault tends to apply to government bills and bonds (which are typicallydenominated in nominal terms), rather than stocks. If one interprets the“risk-free” claim as a government bill, then a higher probability of defaulton bills, conditional on a crisis, lowers the equity premium in a revisedversion of equation 8.
The model also neglects government rationing of consumption duringcrises, notably wars. Rationing can be viewed as a tax on consumption incrisis states. The more effective the system, in the sense of precluding blackmarkets, the higher the effective tax rate on consumption beyond somerationed quantity; thus, a fully enforced rationing system has an infinitetax rate at the margin. (In practice, the situation is complicated becausethe rationing and hence the tax are likely to be temporary, lapsing once thecrisis is over.) Rationing can be viewed as a form of partial default onassets, as above, but one that applies equally to gross returns on stocks andbills. Therefore, although rationing tends to lower the equity premium inan extended version of equation 8, the effects are weaker than those fromcrisis-contingent defaults that apply only to bills.
Another issue for empirical implementation is that the model does notdeal with the duration of disaster states; a disaster is a jump that takes placein one period, which amounts to an instant of time. Our research withNakamura and Steinsson will deal explicitly with the time evolution of theeconomy during disaster states. For present purposes we assume that theimportant aspect of a disaster is the cumulative amount of contraction, b,which we gauge empirically by the numbers shown for C and GDP,respectively, in appendix tables C1 and C2. That is, we assume that, for agiven cumulative decline, the implications for the equity premium do notdepend a great deal on whether this decline occurs in an instant or, morerealistically, is spread out over time.
To illustrate our assumption, figure 3 depicts two possible time pathsfor the log of C. Each case has two normalcy intervals, denoted A and B.These paths reflect growth at 0.025 per year and (different) realizationsof normal shocks with a standard deviation, σ, of 0.02 per year—these parameters apply in our subsequent simulations. In each case a single disas-ter event with a cumulative fractional decline in C by 0.4 happens to occur
ROBERT J. BARRO and JOSÉ F. URSÚA 37
33. See Barro (2006).
ftn. 33
FIG. 3
11302-04_Barro.qxd 8/15/08 5:38 PM Page 37
38 Brookings Papers on Economic Activity, Spring 2008
Figure 3. Paths of Consumption with Different Durations of Crisesa
Source: Authors’ calculations.a. In case 1 a crisis entails a 40 percent decline in C over one period. In case 2 a crisis entails a 40
percent decline in C stretched over four periods. The normalcy periods (A and B in each panel) are generated by assuming mean growth of 0.025 per year with normally distributed shocks that have a standard deviation of 0.02 per year. The paths shown, meant only to be illustrative, reflect different realizations of random numbers in each case.
0.2
0.0
0.6
1.0
0.8
Log of C per capitaCase 1
40% fall
Years
0.4
0.2 0.3 0.4 0.5 0.6 0.7
4
12
16
Log of C per capitaCase 2
Years
8
21 3 4 5 6 7 8 9 10
40% fall
A
A
B
B
11302-04_Barro.qxd 8/15/08 5:38 PM Page 38
in the middle of the sample. We are unsure at present how to model disas-ter states that last for more than an instant. The mean growth rate is likely tobe much lower than normal, and the volatility is likely to be much higherthan normal. In figure 3 the only difference between the two cases is thatthe fractional decline by 0.4 for the disaster in case 1 occurs over one period(which could be one year or one second), whereas that in case 2 stretchesover four periods. The graphs assume, unrealistically, that crises have theusual amount of volatility—that is, normal shocks with σ = 0.02 per year.
Our key assumption is that the determination of expected rates of returnduring normalcy periods (A and B in the two panels of figure 3) is roughlythe same whether disasters look like case 1 or case 2. This conclusionholds in an extension of the model pursued in Barro’s 2006 paper,34 whichassessed the effects of variations in the period length T. (This extension wasfeasible in a model with i.i.d. growth shocks.) In that setting T representsthe fixed duration of a disaster. Variations in T between zero and 5 years didnot have much impact on the implied equity premium (measured per year).
In practice, the normalcy rates of return would not be exactly the samein cases 1 and 2 of figure 3. For example, case 2 implies low, perhaps neg-ative short-term risk-free rates during crises and, therefore, capital gainson longer-term risk-free bonds when a crisis starts. This pattern has impli-cations for the term structure of risk-free rates during normal times. How-ever, a different specification—one where disasters entail higher thanusual chances of default on bonds—predicts capital losses, rather thangains, on longer-term bonds when a crisis occurs. Because of this ambigu-ity, we are unable at this stage to go beyond our assumption that cases 1and 2 are approximately the same for the equity premium.
Simulating the Lucas-Tree Model
We now simulate the Lucas-tree model by viewing the Euler condition inequation 4 as applying to a representative agent at the country level. Thatis, we neglect the implications of imperfect markets and heterogeneousindividuals within countries. However, we also assume that markets arenot sufficiently complete internationally for equation 4 to apply to the rep-resentative agent in the world. In future work we will assess how the analy-sis applies to multiple-country regions, rather than country by country.
In applying equation 4 to the determination of each country’s assetreturns, we neglect any implications from international trade in goods and
ROBERT J. BARRO and JOSÉ F. URSÚA 39
34. Barro (2006, section V).
ftn. 34
11302-04_Barro.qxd 8/15/08 5:38 PM Page 39
assets; that is, we effectively treat each country as a closed economy. Withthis perspective, we can view each country-period observation as pro-viding independent information about the relationship between macro-economic shocks and asset returns. In particular, this independence may beapproximately right despite the clear common international dimensions ofcrises—most obviously from wars but also from financial crises, diseaseepidemics, and natural resource shocks.
We apply the full historical information on disaster probability andsizes to the simulation at each point in time. Thus, we implicitly assumethat the underlying parameters are fixed over time and across countries andare known from the outset to the representative agent in each country. Wetherefore neglect learning about disaster parameters.35
We focus on the model’s implications for the expected rate of return onequity, re, and the risk-free rate, r f, and hence for the equity premium. As itstands, the model is inadequate for explaining the volatility of asset prices,including stock prices. For example, the model unrealistically implies a constant price-dividend ratio and a constant risk-free rate. The mostpromising avenue for extending the model to fit these features—includingthe high volatility of stock returns—is to allow for shifting uncertaintyparameters, notably the disaster probability, p. This possibility is exploredin a recent paper by Xavier Gabaix—his results suggest that the extendedmodel can explain volatility patterns without much affecting the implica-tions for expected rates of return, including the equity premium. In arelated vein, Ravi Bansal and Amir Yaron have pursued the consequencesof shifting expected growth rates, g*.36
The calibrations of the model follow those in the forthcoming paper byBarro. We set the expected normal growth rate, g, at 0.025; the standarddeviation of normal fluctuations, σ, at 0.02; and the reciprocal of theintertemporal elasticity of substitution, θ, at 0.5.37 These choices of param-eters either do not affect the equity premium (g and θ) or have a negligibleimpact (σ). The rate of time preference, ρ, also does not affect the equitypremium. However, ρ (along with g, σ, and θ) affects levels of rates ofreturn, including the risk-free rate, r f (see equations 6 and 7). Given thelack of useful outside information on ρ, we set ρ* in equation 7 to generater f = 0.01—roughly the long-run average across countries of real rates of
40 Brookings Papers on Economic Activity, Spring 2008
35. This issue is stressed by Weitzman (2007).36. Gabaix (2008); Bansal and Yaron (2004).37. For a discussion of the choice of θ, including the problematic nature of estimates
computed from macroeconomic time series, see Barro (forthcoming).
ftn. 35
ftn. 36
ftn. 37
11302-04_Barro.qxd 8/15/08 5:38 PM Page 40
return on bills from table 5.38 Then ρ takes on the value needed to satisfyequation 5.
The calibrations for the disaster probability, p, and the frequency distri-bution of disaster sizes, b, use our multi-country study of disaster events.We can then determine the value of γ needed in equation 8 to replicate anunlevered equity premium of around 0.05—the long-run average acrosscountries implied by the data in table 5. Since we always have r f = 0.01, anunlevered equity premium of 0.05 corresponds to an expected rate ofreturn on unlevered equity, re, of 0.06.
Table 10 reports results of our simulation for crises gauged by C, andtable 11 for those gauged by GDP. For baseline cases, which encompass95 observations of C crises and 152 observations of GDP crises, a coeffi-cient of relative risk aversion, γ, of 3.5 gets the simulated results into theright ballpark for the observed equity premium: specifically, re = 0.059 inthe C case and 0.067 in the GDP case. The respective rates of time prefer-ence, ρ, are 0.045 and 0.052, and the corresponding effective rates of timepreference, ρ*, are 0.029 and 0.037.
The results are sensitive to the choice of γ. For example, the secondlines of tables 10 and 11 show that, if γ = 3.0, the values for re fall to 0.042in the C case and 0.045 in the GDP case.
The results are not very different if the sample encompasses only theOECD countries, in which case the number of C disasters falls from 95 to57, and the number of GDP disasters falls from 152 to 75. The equity pre-mium is still in the right ballpark with γ = 3.5 (or slightly higher for Ccrises).
The results do not change greatly if we truncate the b distribution toeliminate smaller crises. Tables 10 and 11 show the results when, insteadof b ≥ 0.10, we admit only b ≥ 0.15, b ≥ 0.20, b ≥ 0.30, or b ≥ 0.40. Evenwhen b ≥ 0.40, which leaves only eleven C crises and fourteen GDP crises,re is still at 0.047 in the case of C and 0.054 in the case of GDP. Thus, thelarger crises are crucial for getting the equity premium into the right ball-park with a “reasonable” amount of risk aversion, such as γ = 3.5.
This reasoning also applies when we examine nonwar samples, a selec-tion that eliminates the biggest crises from the sample. (We define “war”as applying only to active combatants.) For C crises, the consideration ofa nonwar sample—which retains sixty-six of the original ninety-five
ROBERT J. BARRO and JOSÉ F. URSÚA 41
38. Real rates of return on treasury bills and similar assets are not risk-free and tend par-ticularly to be lower than normal during crises that involve high inflation (see the section on“Asset Returns during Crises” below). Thus, r f may be lower than 0.01. However, peggingto a lower value of r f would not affect our analysis of the equity premium.
ftn. 38
TAB. 10TAB. 11
11302-04_Barro.qxd 8/15/08 5:38 PM Page 41
Tab
le 1
0.
Res
ults
of t
he S
imul
ated
Mod
el B
ased
on
Cons
umer
Exp
endi
ture
Dis
aste
rsa
No.
of
No.
of
disa
ster
-R
ate
of
Spec
ifica
tion
disa
ster
sye
ars
pπ
E(b
)E
(1 −
b)−γ
E(1
−b)
1−γ
ρρ*
retu
rnf r
e
Bas
elin
eb95
343
0.03
630.
277
0.21
93.
882.
340.
045
0.02
90.
059
γ=
3.0
9534
30.
0363
0.27
70.
219
2.96
1.90
0.02
90.
008
0.04
2O
EC
D57
214
0.02
860.
266
0.22
33.
872.
370.
034
0.00
70.
048
Non
-OE
CD
3812
90.
0604
0.29
50.
214
3.89
2.29
0.08
00.
100
0.09
5b≥
0.15
5925
20.
0218
0.23
40.
278
5.28
2.92
0.04
20.
018
0.05
7b≥
0.20
3616
30.
0129
0.22
10.
345
7.41
3.75
0.03
80.
007
0.05
4b≥
0.30
2099
0.00
700.
202
0.43
111
.25
5.17
0.03
5−0
.003
0.05
1b≥
0.40
1160
0.00
380.
183
0.50
616
.90
7.07
0.03
1−0
.015
0.04
7N
onw
ar66
208
0.02
400.
317
0.16
82.
011.
630.
004
−0.0
510.
016
Non
war
, γ=
966
208
0.02
400.
317
0.16
87.
705.
870.
037
−0.0
380.
053
HP
-filt
ered
4327
10.
0167
0.15
90.
232
3.68
2.35
0.01
6−0
.030
0.03
0H
P-fi
lter
ed, γ
=4.
543
271
0.01
670.
159
0.23
26.
183.
680.
034
−0.0
120.
050
Sour
ce: M
odel
sim
ulat
ions
by
the
auth
ors.
a. U
nles
s ot
herw
ise
spec
ified
, the
coe
ffici
ent o
f re
lativ
e ri
sk a
vers
ion,
γ, i
s se
t at 3
.5; a
nd th
e th
resh
old
for
the
disa
ster
siz
e, b
,at 0
.10.
Cal
ibra
ted
para
met
ers
com
mon
to a
ll sp
ec-
ifica
tions
are
as
follo
ws:
exp
ecte
d no
rmal
gro
wth
rat
e g=
0.02
5; s
tand
ard
devi
atio
n of
nor
mal
fluc
tuat
ions
σ=
0.02
; rec
ipro
cal o
f in
tert
empo
ral e
last
icity
of
subs
titut
ion θ=
0.5,
as
disc
usse
d in
the
text
. The
ris
k-fr
ee r
ate
rfis
0.0
1 in
all
case
s.b.
Sam
ple
cons
ists
of
all C
dis
aste
rs f
or th
e tw
enty
-fou
r in
clud
ed c
ount
ries
fro
m ta
ble
C1
in a
ppen
dix
C.
c. p
is th
e es
timat
ed p
roba
bilit
y pe
r ye
ar o
f m
ovin
g fr
om n
orm
alcy
to d
isas
ter,
and
πth
e es
timat
ed p
roba
bilit
y pe
r ye
ar o
f m
ovin
g fr
om d
isas
ter
to n
orm
alcy
.d.
E(b
) is
the
mea
n di
sast
er s
ize;
E(1
−b)
−γan
d E
(1 −
b)1−
γar
e, r
espe
ctiv
ely,
the
mea
n va
lues
of
thes
e ke
y de
term
inan
ts o
f th
e eq
uity
pre
miu
m, f
rom
equ
atio
n 8
in th
e te
xt.
e. ρ
is th
e ra
te o
f tim
e pr
efer
ence
and
ρ*
is th
e ef
fect
ive
rate
of
time
pref
eren
ce g
iven
in e
quat
ion
5; v
alue
s ar
e ch
osen
to g
ener
ate
rf=
0.01
in e
quat
ion
7.f.
Ove
rall
expe
cted
rat
e of
ret
urn
on u
nlev
ered
equ
ity, f
rom
equ
atio
n 6.
Mom
ents
of d
isas
ter
size
dT
ime
pref
eren
cee
Pro
babi
liti
es
11302-04_Barro.qxd 8/15/08 5:38 PM Page 42
Tab
le 1
1.
Res
ults
of t
he S
imul
ated
Mod
el B
ased
on
GD
P D
isas
ters
No.
of
No.
of
disa
ster
-R
ate
of
Spec
ifica
tion
disa
ster
sye
ars
pπ
E(b
)E
(1 −
b)−γ
E(1
−b)
1−γ
ρρ*
retu
rn r
e
Bas
elin
ea15
253
00.
0369
0.28
70.
207
4.03
2.31
0.05
20.
037
0.06
7γ=
3.0
152
530
0.03
690.
287
0.20
72.
991.
860.
032
0.01
00.
045
OE
CD
7526
30.
0287
0.28
50.
221
4.96
2.60
0.05
70.
039
0.07
3N
on-O
EC
D77
267
0.05
090.
288
0.19
43.
132.
040.
043
0.03
30.
057
b≥
0.15
8332
00.
0192
0.25
90.
278
6.08
3.09
0.04
80.
022
0.06
3b≥
0.20
5422
90.
0122
0.23
60.
338
8.31
3.90
0.04
50.
014
0.06
1b≥
0.30
2411
50.
0053
0.20
90.
453
15.3
26.
230.
041
0.00
10.
057
b≥
0.40
1469
0.00
310.
203
0.53
223
.13
8.63
0.03
8−0
.007
0.05
4N
onw
ar11
237
00.
0261
0.30
30.
168
2.02
1.64
0.00
5−0
.048
0.01
7N
onw
ar, γ
=9
112
370
0.02
610.
303
0.16
87.
916.
010.
042
−0.0
180.
059
HP
-filt
ered
7044
60.
0174
0.16
00.
224
4.08
2.42
0.02
2−0
.022
0.03
6H
P-fi
lter
ed, γ
=4.
070
446
0.01
740.
160
0.22
45.
553.
090.
035
−0.0
080.
050
Sour
ce: M
odel
sim
ulat
ions
by
the
auth
ors.
a. S
ampl
e co
nsis
ts o
f al
l GD
P di
sast
ers
for
the
thir
ty-s
ix in
clud
ed c
ount
ries
fro
m ta
ble
C2
in a
ppen
dix
C. S
ee th
e no
tes
to ta
ble
10 f
or d
iscu
ssio
n an
d de
finiti
ons.
Mom
ents
of d
isas
ter
size
Tim
e pr
efer
ence
Pro
babi
liti
es
11302-04_Barro.qxd 8/15/08 5:38 PM Page 43
disasters—yields r e = 0.016. For GDP crises, with 112 of the original 152disasters retained, the result is r e = 0.017. Getting into the right ballparkhere for the equity premium requires a much higher coefficient of relativerisk aversion, γ. For example, tables 10 and 11 show that γ = 9 yields r e =0.053 for C and 0.059 for GDP.
As discussed before, we redid the analysis using trend values of log(C)and log(GDP) calculated from HP filters. As already noted, this methodcaptures in an informal way the idea that crises may have less than perma-nent effects on levels of C and GDP. Tables 10 and 11 show that the HP fil-tering reduces the number of C disasters from 95 to 43 and of GDPdisasters from 152 to 70. Correspondingly, the estimated disaster probabil-ities fall from 0.0363 to 0.0167 for C and from 0.0369 to 0.0174 for GDP.However, the size distributions of the crises are not so different from thebaseline cases. For C crises the mean of b is 0.232, rather than 0.219, andfor GDP the mean is 0.224, rather than 0.207. Hence, the HP filteringdecreases the number of disasters but slightly raises the average size, con-tingent on the occurrence of a disaster.
If we again use a coefficient of relative risk aversion, γ, of 3.5, the HPfiltering lowers the computed re to 0.030 for the C case and to 0.036 forthe GDP case. However, γ does not have to increase very much to restore areasonable equity premium. For example, for C crises, γ = 4.5 yields r e =0.050, whereas for GDP crises, γ = 4 yields r e = 0.050.
In terms of broad patterns, the results based on C in table 10 deliverresults for the equity premium that are similar to those based on GDP intable 11. On the one hand, this finding suggests a certain robustness, in thatthe results are not sensitive to measurement differences in these two mainmacroeconomic aggregates. On the other hand, it means that fitting theequity premium does not depend on our efforts in measuring consumerexpenditure and thereby getting closer to measures of consumption.
Overall, the simulations in tables 10 and 11 show that the model deliversreasonable equity premia with “plausible” coefficients of relative risk aver-sion for a variety of specifications. The main lack of robustness applies toelimination of the biggest crises from the sample, for example, by remov-ing the war-related crises.
Asset Returns during Crises
In our Lucas-tree model of asset returns, crises feature downward jumpsin C and GDP at a point in time. More realistically, they fall graduallyduring crises of varying lengths, as suggested by figure 3. In our empiri-
44 Brookings Papers on Economic Activity, Spring 2008
11302-04_Barro.qxd 8/15/08 5:38 PM Page 44
cal analysis, we approximated the crisis declines in C and GDP by cumu-lative fractional amounts over peak-to-trough intervals, as shown inappendix tables C1 and C2 and figures 1 and 2. Now we carry out a pre-liminary analysis that considers observed returns during crises on stocksand bills.
Stock Returns during Crises
In the theory, real stock prices jump down discretely at the start of acrisis. More realistically, stock prices would fall each time negativeinformation hits the financial markets. Since we are conditioning oncrises that cumulate to at least a 10 percent fall in C or GDP, the crisestypically feature more than one adverse piece of news (or, rather, morenegative than positive news). Thus, the stock-price declines tend also tobe spread out during the crises. By analogy to our procedure for measur-ing decreases in C and GDP, we measure the crisis changes in stockprices by cumulative fractional amounts. Specifically, the real stock-price falls shown in appendix tables C1 and C2 are the total fractionaldeclines from the end of the year before the peak to the end of the yearbefore the trough. (Negative values indicate stock-price increases.) Thisprocedure omits changes in stock prices during the trough year, when thefinancial markets would likely be influenced by information indicatingthat the crisis had ended.
Data on real stock prices are available for only a subset of the C andGDP crises: 54 of the 95 C crises (appendix table C1) and 72 of the 152GDP crises (table C2). The majority of these crises show declines in realstock prices: in forty-two of the fifty-four C events (78 percent) and fifty-five of the seventy-two GDP events (76 percent). Figure 4 shows the sizedistribution of real stock-price declines during crises (where negativevalues correspond to stock-price rises). The left-hand panels show the fulldistributions, and the right-hand panels consider only the stock-pricedecreases. The left-hand panels have two outliers with very large priceincreases: Argentina in the late 1980s and Chile in the mid-1970s. In thesesituations, periods of economic contraction were accompanied by majorcontemporaneous or prospective reforms that were viewed favorably bythe stock markets.39 To admit the possibility of stock-price increases dur-ing crises into the model, we would have to expand the framework to allow
ROBERT J. BARRO and JOSÉ F. URSÚA 45
39. An analogous situation is the C crisis in Venezuela in the late 1980s (see appendixtable C1), which, however, is not included in the sample currently being considered.
FIG. 4
ftn. 39
11302-04_Barro.qxd 8/15/08 5:38 PM Page 45
46 Brookings Papers on Economic Activity, Spring 2008
Source: See table 4.a. The sample for consumer expenditure, C, disasters is the 54 of 95 cases for included countries from
table C1 with data on stock-price changes. The sample for GDP disasters is the 72 of 152 cases for included countries from table C2 with data on stock-price changes. We exclude cases in which missing data cause the period for stock-price changes to deviate from that for the declines in C or GDP.
b. Negative numbers indicate increases in real stock prices.
4
8
12
16
4
8
12
16
20
–3 –2 –1 0
–3 –2 –1 0 1
Cumulative fractional real declineb Cumulative fractional real decline
Cumulative fractional real declineCumulative fractional real declineb
No. of eventsAll C disasters
All C disasters
C disasters in whichstock prices declined
GDP disasters in whichstock prices declined
No. of events
No. of events No. of events
Mean = 0.086Median = 0.172
Mean = 0.327Median = 0.288
Mean = 0.376Median = 0.374
Mean = 0.165Median = 0.294
1
2
3
4
5
0.1 0.2 0.3 0.4 0.5 0.6 0.7
1
2
3
4
5
0.2 0.4 0.6 0.80.1 0.3 0.5 0.7
Figure 4. Distributions of Real Stock-Price Declines during Consumer Expenditure and GDP Disastersa
for shocks to parameters, such as the expected growth rate, g*, or thedisaster probability, p.
The mean and median of fractional stock-price declines were 0.086 and0.172, respectively, for C crises and 0.165 and 0.294 for GDP crises. Con-ditioning on cases of stock-price decrease in the right-hand panels of fig-ure 4 shows roughly uniform shapes for the frequency distributions in the
11302-04_Barro.qxd 8/15/08 5:38 PM Page 46
ROBERT J. BARRO and JOSÉ F. URSÚA 47
40. Recall that the samples are selected by considering C or GDP declines of 0.10 ormore. We could instead select the sample by considering real stock-price declines of 0.10 ormore. Our conjecture is that the size distributions would then look like power-law functions,as in figures 1 and 2.
41. An additional difficulty is the imperfect matching of the timing of stock-pricechanges with the timing of the declines in C or GDP. In our data, stock-price changes arefrom the end of the year before the peak to the end of the year before the trough. Thechanges in C or GDP are from the peak year to the trough year, with C and GDP represent-ing annual flows for each year.
ftn. 41, tab. 12
range of sizes between zero and 0.7.40 In this range the mean and themedian of stock-price declines were 0.327 and 0.288, respectively, for Ccrises and 0.376 and 0.374 for GDP crises.
In tables 10 and 11 we simulated the underlying asset pricing modelusing the observed distributions of C and GDP crises. The underlyingassumption was that the size of the fractional stock-price decline (forunlevered equity) during a crisis equaled the size of the fractional decline,b, in C or GDP. We can instead simulate the model by using the actualstock-price changes during crises, as shown in appendix tables C1 and C2and in figure 4. Since these stock returns refer to levered equity, these cal-culations apply to expected returns on levered equity.
The asset pricing condition in equation 4 involves the term E[Rt � (1 − b)−γ], where Rt is the gross real stock return during crises, and b is thefractional decline in C or GDP during crises. This expression is difficult tocalculate accurately because stock-price changes are highly volatile, par-ticularly during crises.41 In table 12 we compute this term in four alterna-tive ways. First, we measure contractions by either C or GDP, and second,we use either the full distributions of stock-price changes (the left-handpanels of figure 4) or the truncated distributions that consider only stock-price declines (the right-hand panels). This last choice is more consistentwith our model and may also lessen the effects from measurement error.
The calculations using the full distributions of stock-price changes donot accord well with observed long-term average returns on levered equityof around 0.081 (from table 5). If we use γ = 3.5, as before, the simulationsin table 12 deliver an overall mean rate of return on levered equity of 0.029based on C crises and 0.031 based on GDP crises. The results fit better if weuse the truncated distributions, which eliminate cases of stock-priceincrease during crises. The simulated mean rate of return on levered equityis then 0.075 based on C crises and 0.034 based on GDP crises. Given thewide range of results, we cannot, at this stage, reach firm conclusions fromour attempts to simulate the model using observed stock-price changes dur-ing crises.
ftn. 40
11302-04_Barro.qxd 8/15/08 5:38 PM Page 47
Bill Returns during Crises
In the Lucas-tree model, the risk-free rate is the same in normal times asin a crisis, which lasts an instant of time. The same pattern would apply tothe expected real rate of return on short-term bills—the type of claim con-sidered in table 5—if we introduce a constant probability of default or, fornominal claims, a time-invariant process for inflation.
48 Brookings Papers on Economic Activity, Spring 2008
Table 12. Results of the Simulated Model Using Actual Stock-Price Changes during Crisesa
C crises GDP crises
All crises Crises with All crises Crises with with stock stock-price with stock stock-price
data decreases only data decreases only
No. of observations 54 42 72 55Coefficient of relative 3.5 3.5 3.5 3.5
risk aversion γEffective time-preference 0.029 0.029 0.037 0.037
rate ρ*Normal growth rate g 0.025 0.025 0.025 0.025(1 + g)−γ 0.917 0.917 0.917 0.917Disaster probability p 0.0363 0.0363 0.0369 0.0369
Stock returnsd
Overall mean E(Rt − 1) 0.0814 0.0814 0.0814 0.0814(from table 5)
Mean of crisis sample −0.0864 −0.3272 −0.1655 −0.3759E(Rt − 1)
Mean of crisis sample 3.446 1.964 3.545 3.235E[Rt� (1 − b)−γ]
Model simulationImplied noncrisisb 0.035 0.090 0.038 0.050
E(Rt − 1)Implied overall meanc 0.029 0.075 0.031 0.034
E(Rt − 1)
Source: Authors’ calculations.a. The parameters γ, ρ*, g, and p come from tables 10 and 11. Stock-price changes during crises are
reported in tables C1 and C2. The four crisis samples used are C crises with data on stock-price changes(N = 54), C crises with stock-price decreases (N = 42), GDP crises with data on stock-price changes (N = 72), and GDP crises with stock-price decreases (N = 55).
b. Based on the following approximate formula, derived from equations 2 through 4 in the text(neglecting the effects from normal fluctuations, σ):
c. Based on the formula E(Rt) = p � (ERt)⎟ crisis + (1 − p) � (ERt)⎟ noncrisis.d. “Mean of crisis sample E(Rt − 1)” is the mean for each crisis sample of the fractional change in real
stock prices. “Mean of crisis sample E[Rt � (1 − b)−γ]” is the mean for each crisis sample of the interactionbetween (1 + fractional change in real stock prices) and (1 − b)−γ, where b is the fractional decline inC or GDP.
1 1 1 1+ ≈ +( ) −( )⎡⎣
⎤⎦ + −( )− −ρ γ γ
* g pE R b p Etcrisis
i i i RRt noncrisis( )⎧⎨⎩
⎫⎬⎭
.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 48
Observed returns on short-term bills deviate from these predictions.Table 13 shows means and medians for real bill returns during the C andGDP crises in appendix tables C1 and C2. (The bill returns for each crisisare mean values from the peak year to one year before the trough year.)These results apply to the main samples (95 C crises and 152 GDP crises)when data are also available on bill returns (58 for C crises and 73 for GDPcrises). The average real bill return during crises was between −2 percentand −5 percent a year, depending on whether a C or a GDP sample is usedand on whether the mean or the median is considered. Hence, the averagecrisis return was below the long-term average of around 1 percent shownin table 5.
There are two main issues to consider. The first is whether a substan-tially negative number, such as −2 percent to −5 percent a year, is a goodmeasure of expected real bill returns during crises. A major question hereconcerns inflation. The second is whether our analysis of the equity pre-mium would be much affected if the expected real return on bills duringcrises were substantially negative. Since the second issue is more funda-mental, and we think the answer is no, we consider that question first.
One possible reason for a low equilibrium expected real bill return dur-ing crises, suggested by figure 3, is that crisis states last for more than aninstant, and the mean growth rate of C in these states is negative. (A sup-porting reason, not shown in figure 3, is that volatility tends to be unusu-ally high in crisis states.) In these cases the risk-free rate and the expectedreal bill return would be unusually low in crises. However, the key issuefor the equity premium is not the low level of the real bill return duringcrises (caused by a low expected growth rate or some other factor) but,rather, whether the incidence of a crisis imposes substantial real capitallosses on bills. Recall that bills correspond, empirically, to claims withmaturity of three months or less. Although the crisis-induced changes inthe real value of these claims are hard to measure accurately, substantial
ROBERT J. BARRO and JOSÉ F. URSÚA 49
Table 13. Bill Returns and Inflation Rates during Crisesa
C crises GDP crises
Item N Mean Median N Mean Median
Real rate of return on bills 58 −0.051 −0.023 73 −0.052 −0.021Inflation rate 87 1.13 0.066 123 0.961 0.069
Source: Authors’ calculations.a. The results apply to the crisis samples used in the main analysis: 95 C crises from table C1 and 152
GDP crises from table C2. Data for real rates of return on bills and inflation rates are for the subsamplesthat also have data on bill returns or inflation rates, as indicated in tables C1 and C2. The cells showmeans and medians of real rates of return on bills and inflation rates for these subsamples.
TAB. 13
11302-04_Barro.qxd 8/15/08 5:38 PM Page 49
real capital losses can arise only if there are jumps in the price level or lit-eral defaults on bills. Absent these effects, the pricing of bills in normaltimes (and, hence, the equity premium) would not be much influenced bythe prospect of low equilibrium real bill returns during crises.42 In contrast,for long-term bonds, changes in real capital values at the onsets of crisesmay be substantial and would have to be compared with those on stocks.Thus it would be useful to analyze the crisis experiences of the ten-yeargovernment bonds included in table 5. However, the measurement ofcrisis-induced changes in real bond values will be challenging.
A different point is that the computed averages of real bill returns dur-ing crises may understate expected real returns because of influences frominflation. Crises do feature higher than usual inflation rates: table 13 showsthat the median inflation rates were 6.6 percent for C crises and 6.9 percentfor GDP crises, compared with 4.2 percent for long samples for all coun-tries taken together.43 Hence, one possible explanation for the low averagereal bill return during crises is that the greater incidence of high inflationcorresponds to high unanticipated inflation and, thereby, to a shortfallof realized real returns on nominally denominated bills from expectedreturns. A shortcoming of this argument is that it requires inflation to besystematically underestimated during crises (which are presumably recog-nized contemporaneously).
A second possibility is that the reported nominal yields at times of highinflation systematically understate the true nominal returns and, therefore,lead to underestimates of the real returns. The reason is the understatementof the implications of compounding for calculating true nominal returns.44
50 Brookings Papers on Economic Activity, Spring 2008
42. An analogous result holds for paper currency. The expected real return on currencywould be low during a crisis if the expected inflation rate were high. However, absent jumpsin the price level or literal defaults, currency held in normal times would still provide goodprotection against crisis-induced stock-market crashes.
43. The inflation rate for each crisis in tables C1 and C2 is the mean value from the peakyear to one year before the trough year.
44. As an example, Peru’s crisis in 1987–92 featured very high inflation. In 1989 theprice level increased by a factor of 29. The International Monetary Fund’s InternationalFinancial Statistics (IFS) reports, on a monthly basis, nominal deposit yields for 1989 aver-aging 1,100 percent a year. The IFS staff tell us that an annual rate of 1,100 percent meansthat the nominal value of funds held as deposits would rise over a year by a factor of 12. Thisnominal return, in conjunction with the inflation experience, produces a real rate of returnfor Peru in 1989 of −0.58 per year. Suppose, alternatively, that a nominal yield of 1,100 per-cent means that returns are compounded monthly at a rate of 92 percent (= 1,100/12) permonth. In this case the nominal value would rise over a year by a factor of 2,500, implyingan astronomically positive real rate of return. The point is that when the inflation rate is high,compounding errors of this type have large implications for calculated real rates of return—and we think that these errors are regularly in the direction of understating true returns.
ftn. 42
ftn. 43
ftn. 44
11302-04_Barro.qxd 8/15/08 5:38 PM Page 50
We think that this issue is quantitatively important, and we are attemptingto improve our calculations in this regard.
Plans for Further Research
We plan in future research to expand the twenty-four-country sample for Cand the thirty-six-country sample for GDP. Promising candidates areMalaysia and Singapore, both of which have gaps in the data aroundWorld War II. Also promising are Russia back to the pre-World War Itsarist period, and Turkey back to the times of the Ottoman Empire, forwhich we currently have data since 1923. We are also considering Ireland,particularly whether we can isolate macroeconomic data for the territory ofthe Republic of Ireland from U.K. statistics for the period preceding Irishindependence in 1922. We plan also to reexamine the pre-1929 U.S. data,focusing on the Civil War years.
We will try to go further in measuring the division of personal con-sumer expenditure between durables versus nondurables and services.Appendix table C3 shows the data that we have been able to compile thusfar for crisis periods. We may also attempt to add data on government con-sumption. A key issue here is the separation of military outlays from otherforms of government consumption expenditure.
We plan to construct time series for C and GDP per capita at the levels ofregions that include multiple countries: the OECD, Western Europe, LatinAmerica, Asia, the “world,” and so on. These regional aggregates can berelevant when countries are integrated through financial and other markets.There are tricky aspects of this exercise involving changes in country bor-ders, and we are working on this issue. Once we have these superaggregatevariables, we will examine C and GDP crises at regional levels.
In joint work with Rustam Ibragimov, we will use the method of Gabaixand Ibragimov to estimate the distribution of disaster sizes, b, within apower-law context.45 Preliminary analysis shows good results when treat-ing the transformed variable 1/(1 − b) as subject to a power-law densityfunction with exponent α. With these results we can compute the keyexpectations that enter into the theoretical model, such as E(1 − b)−γ, asfunctions of γ and α. Preliminary results suggest that the estimated α,around 5, is consistent with a finite value of E(1 − b)−γ, when γ is around3.5. With these results, we can redo the simulation of the model using thefitted density function for b, rather than the observed histogram.
ROBERT J. BARRO and JOSÉ F. URSÚA 51
45. Gabaix and Ibragimov (2007).
ftn. 45
11302-04_Barro.qxd 8/15/08 5:38 PM Page 51
We are working with Emi Nakamura and Jón Steinsson on a formal sta-tistical model of the evolution of consumer expenditure and GDP. Wewill use the full time series on C and GDP to estimate the probability ofdisaster (possibly time-varying), the evolution of economic contractionsduring disaster states, the probability of return to normalcy, and the long-run effects of disasters on levels and growth rates of C and GDP. We willalso allow for trend breaks in growth rates, as well as for some differencesin uncertainty parameters across countries and over time.
We are working with Emmanuel Farhi and Xavier Gabaix on a differentapproach to measuring time-varying disaster probabilities. Our plan isto use U.S. data since the early 1980s on prices of stock-index options togauge changing market perceptions of the likelihood of substantial adverseshocks. In addition to considering the equity premium, we will applythis analysis to the bond-bill premium, which we found to be about 1 per-cent a year.
ACKNOWLEDGMENTS The National Science Foundation has sup-ported this research. We thank for suggestions Olivier Blanchard, JohnCampbell, George Constantinides, Emmanuel Farhi, Xavier Gabaix, ClaudiaGoldin, Rustam Ibragimov, Dale Jorgenson, Emi Nakamura, and JónSteinsson. We appreciate help with the financial data from Bryan Taylor ofGlobal Financial Data. On the construction of the database on GDP andpersonal consumer expenditure, we are grateful for comments and contribu-tions from many people worldwide. A nonexhaustive list includes RobertoCortés (Argentina); Felix Butschek, Anton Kausel, Felix Rauscher, MarcusSchleibecker, and Rita Schwarz (Austria); Frans Buelens, Erik Buyst,Jean-Jacques Heirwegh, Yves de Lombaerde, Kim Oosterlinck, PeterScholliers, Yves Segers, Eric Vanhaute, and Guy Vanthemsche (Belgium);Claudio Haddad (Brazil); José Diaz and Eric Haindl (Chile); AdolfoMeisel, Carlos Posada, and Miguel Urrutia (Colombia); Jakob Madsen(Denmark); Riitta Hjerppe and Visa Heinonen (Finland); Claude Diebolt,Thomas Piketty, Gilles Postel-Vinay, and Pierre Villa (France); CarstenBurhop, Davide Cantoni, Nicola Fuchs-Schündeln, Albrecht Ritschl,Mark Spoerer, Beatrice Weder, and Guntram Wolff (Germany); ViolettaHionidou, George Kostelenos, and George Manolas (Greece); GuðmundurJónsson (Iceland); Mausumi Das, Ramesh Kolli, Bharat Ramaswami,Bhanoji Rao, Partha Sen, S. L. Shetty, Rohini Somanathan, and NittalaSubrahmanyasastry (India); Ann Booth, Pierre van der Eng, and Keesvan der Meer (Indonesia); Stefano Fenoaltea (Italy); Yana Kandaiya,
52 Brookings Papers on Economic Activity, Spring 2008
11302-04_Barro.qxd 8/15/08 5:38 PM Page 52
H. R. H. Raja Nazrin, and Wan Rahim Wan Ahmad (Malaysia); AuroraGómez, Stephen Haber, Sandra Kuntz, Jaime de la Llata, GracielaMárquez, and John Womack (Mexico); Marjan Balkestein, Ferry Lapré,Herman de Jong, Hein Klemann, Jan-Pieter Smits, and Jan Luiten vanZanden (Netherlands); Brian Easton, Anthony Endres, Les Oxley, AndrewPetty, Jakob Preston, Keith Rankin, Grant Scobie, and John Singleton(New Zealand); Ola Grytten and Karin Snesrud (Norway); José Robles(Peru); Ricardo Jose and Richard Hooley (Philippines); Luzia Estevens,Pedro Lains, and José Tavares (Portugal); Paul Gregory (Russia); IchiroSugimoto (Singapore); Olu Akimboade and Jon Inggs (South Africa);Myung-Soo Cha, Nak-Nyeon Kim, Mitsuhiko Kimura, Jong-Wha Lee,and Dwight Perkins (South Korea); Leandro Prados (Spain); RodneyEdvinsson (Sweden); Felix Andrist, Philippe Bacchetta, Stefan Gerlach,and Stefanie Schnyder (Switzerland); Sevket Pamuk (Turkey); and JorgeAlvarez and Inés Morales (Uruguay). Many other researchers providedinvaluable contributions through their published work. All errors remainour own.
ROBERT J. BARRO and JOSÉ F. URSÚA 53
11302-04_Barro.qxd 8/15/08 5:38 PM Page 53
Tab
le A
1.
Mai
n D
iffe
renc
es b
etw
een
Mad
diso
n’s
GD
P D
ata
and
Dat
a U
sed
in T
his
Pape
r
Cou
ntry
Foc
us p
erio
dM
addi
son
(upd
ated
ver
sion
)O
ur a
ppro
ach
Arg
enti
na
Aus
tria
Bra
zil
Bel
gium
Lat
e 19
thce
ntur
y(1
870–
1900
)
Wor
ld W
ar I
I(1
944–
46)
19th
–20t
hce
ntur
ies
19th
–20t
hce
ntur
ies
(185
0–90
)
Wor
ld W
ar I
(191
4–19
)
Wor
ld W
ar I
I(1
939–
47)
Ben
chm
ark
valu
es p
rovi
ded
only
for
187
0 an
d 18
90;
appa
rent
ly c
alcu
late
d by
assu
min
g sa
me
grow
th r
ates
as in
190
0–13
.In
dica
ted
sour
ce d
oes
not
cont
ain
figu
re f
or 1
945;
esti
mat
ion
proc
edur
e is
undi
sclo
sed.
Adj
usts
the
seri
es to
pre
sent
-da
y bo
unda
ries
of
Aus
tria
.
Pre
sent
s a
line
ar tr
end
for
1870
–90
(div
erge
nce
wit
hre
spec
t to
sour
ce is
unex
plai
ned)
. Mis
sing
1851
–69.
Ass
umed
to m
ove
in ta
ndem
wit
h F
ranc
e.
Ass
umed
to m
ove
in ta
ndem
wit
h F
ranc
e.
Use
d va
riou
s so
urce
s, in
clud
ing
rece
ntly
pub
lish
ed s
erie
s ba
sed
on s
ecto
ral
outp
ut f
or e
arli
er d
ecad
es (
incl
udin
g ag
ricu
ltur
e, m
inin
g, m
anuf
actu
ring
,en
ergy
, con
stru
ctio
n, tr
ade,
tran
spor
ts, a
nd s
ervi
ces)
. Suf
fici
ent c
over
age
allo
ws
star
ting
the
seri
es in
187
5.
Est
imat
ed g
row
th r
ates
for
194
4–46
usi
ng a
wei
ghte
d av
erag
e of
inde
xes
ofin
dust
rial
pro
duct
ion
and
live
stoc
k pr
oduc
tion
(th
e la
tter
as
prox
y fo
r th
eag
ricu
ltur
al s
ecto
r); e
stim
ates
wer
e co
nstr
aine
d to
fit t
he g
row
th r
ate
betw
een
benc
hmar
k va
lues
pro
vide
d in
the
orig
inal
sou
rce.
Fol
low
ed th
e cr
iter
ion
expl
aine
d in
the
text
for
terr
itor
ial a
djus
tmen
t; o
utpu
tm
easu
res
corr
espo
ndin
g to
the
Aus
tro-
Hun
gari
an E
mpi
re w
ere
used
up
to19
18 a
nd to
Aus
tria
fro
m th
en o
nwar
d.C
onst
ruct
ed a
con
tinu
ous
seri
es s
tart
ing
in 1
850
com
bini
ng v
ario
us s
ourc
es,
amon
g th
em th
e m
ost r
ecen
t rev
isio
n of
Bra
zili
an G
DP
for
the
20th
cen
tury
that
is c
urre
ntly
ava
ilab
le, w
hich
dif
fers
fro
m th
e ea
rlie
r es
tim
ates
use
d in
Mad
diso
n’s
seri
es.
Est
imat
ed b
ased
on
the
wei
ghte
d m
ovem
ent i
n pr
oduc
tion
of
carb
on, c
ast i
ron,
stee
l, an
d pr
oxie
s fo
r ag
ricu
ltur
al o
utpu
t in
the
form
of
avai
labl
e ca
ttle
and
impo
rted
mal
t for
bre
wer
ies.
Tre
nds
wer
e m
atch
ed w
ith
prod
ucti
vity
dat
a in
the
carb
on in
dust
ry, n
umbe
r of
met
allu
rgic
al f
acil
itie
s in
ope
rati
on, a
ndun
empl
oym
ent fi
gure
s.E
stim
ated
bas
ed o
n be
nchm
ark
valu
es c
onst
ruct
ed u
sing
dat
a on
indu
stri
alac
tivi
ty in
dexe
s an
d pr
oduc
tion
of
carb
on, s
teel
, and
ele
ctri
city
, in
com
bina
tion
wit
h tr
ansp
orts
dat
a. W
hen
indu
stri
al d
ata
wer
e m
issi
ng,
info
rmat
ion
on r
ailr
oads
, veh
icle
s, a
nd tr
ansp
orta
tion
of
mer
chan
dise
and
pass
enge
rs, a
mon
g ot
her
com
mun
icat
ions
indi
cato
rs, w
ere
wei
ghte
d to
conn
ect b
ench
mar
k va
lues
.
AP
PE
ND
IX A
11302-04_Barro.qxd 8/15/08 5:38 PM Page 54
Col
ombi
a
Den
mar
k
Fra
nce
Ger
man
y
Gre
ece
1901
–12
19th
–20t
hce
ntur
y
19th
–20t
hce
ntur
ies
(Wor
ld
War
s I
& I
I)
Wor
ld W
ar I
I(1
944–
46)
19th
–20t
hce
ntur
ies
19th
–20t
hce
ntur
ies
(191
4–20
)
Ser
ies
inte
rpol
ated
wit
hav
erag
e m
ovem
ent i
n B
razi
lan
d C
hile
.S
tart
s 18
20; t
erri
tori
alad
just
men
t to
elim
inat
eim
pact
of
Nor
th S
chle
swig
.S
erie
s in
terp
olat
ed b
etw
een
1913
and
192
0 ba
sed
onfi
gure
s of
indu
stri
al a
ndag
ricu
ltura
l out
put (
assu
min
gse
rvic
es r
emai
ned
stab
le);
inte
rpol
ated
bet
wee
n 19
38an
d 19
49 u
sing
info
rmat
ion
from
a s
epar
ate
repo
rt o
nna
tion
al in
com
e.A
ssum
es 1
945
valu
e la
ym
idw
ay b
etw
een
1944
and
1946
val
ues;
figu
res
for
thes
e tw
o ye
ars
are
link
edfr
om o
rigi
nall
y un
conn
ecte
dso
urce
s.B
asel
ine
seri
es is
adj
uste
d to
fit b
orde
rs in
thre
e po
ints
inti
me.
Fiv
e be
nchm
ark
valu
es a
regi
ven
for
1820
–192
1(m
issi
ng 1
914–
20).
App
aren
tly,
as
in a
n ol
der
but c
onti
nuou
s ve
rsio
n of
Mad
diso
n’s
seri
es, t
hese
benc
hmar
ks a
re a
ssum
ed to
foll
ow th
e ag
greg
ate
for
Eas
tern
Eur
ope.
Use
d ac
tual
GD
P e
stim
ates
for
Col
ombi
a st
arti
ng f
rom
190
5 an
d co
nstr
ucte
dfr
om th
e pr
oduc
tion
sid
e.
Cho
se a
dif
fere
nt c
ombi
nati
on o
f so
urce
s (s
erie
s st
arts
in 1
818)
. Ter
rito
rial
adju
stm
ent t
o fo
llow
cri
teri
on e
xpla
ined
in m
ain
text
.
A d
iffe
rent
set
of
sour
ces
was
cho
sen
so a
s to
hav
e G
DP
mea
sure
s co
nsis
tent
wit
h th
e pr
ivat
e co
nsum
ptio
n se
ries
that
wou
ld b
e bu
ilt i
n pa
rall
el. M
ore
rece
nt a
nd r
evis
ed m
easu
res
of th
e ev
olut
ion
of o
utpu
t dur
ing
the
wor
ld w
ars
wer
e pr
efer
red.
The
se a
re r
efine
men
ts o
f th
e of
fici
al s
erie
s pr
oduc
ed b
y th
eF
renc
h In
stit
ute
of S
tati
stic
s an
d E
cono
mic
s.
Use
d le
vel-
com
para
ble
anch
or v
alue
s fo
r 19
44 a
nd 1
946.
Est
imat
ed c
hang
esfo
r 19
45 a
nd 1
946
base
d on
rec
entl
y pu
blis
hed
data
on
indu
stri
al p
rodu
ctio
nfo
r W
est a
nd E
ast G
erm
any,
in c
ombi
nati
on w
ith
data
on
agri
cult
ural
out
put
(cro
ps a
nd li
vest
ock)
.
Fol
low
ed th
e cr
iter
ion
expl
aine
d in
the
text
for
terr
itor
ial a
djus
tmen
t: s
moo
thpa
stin
g of
per
cap
ita
grow
th r
ates
dur
ing
tran
siti
on y
ears
of
sepa
rati
on a
ndun
ifica
tion
.U
sed
a co
ntin
uous
and
long
er ti
me
seri
es b
ased
on
new
est
imat
es d
evel
oped
by
a gr
oup
of r
esea
rche
rs f
rom
the
Cen
tre
for
Pla
nnin
g an
d E
cono
mic
Res
earc
hto
geth
er w
ith
the
His
tori
cal A
rchi
ves
of th
e N
atio
nal B
ank
of G
reec
e, b
ased
on o
utpu
t in
prim
ary,
sec
onda
ry, a
nd te
rtia
ry a
ctiv
itie
s, s
ecto
ral w
eigh
ts,
pric
e de
flat
ors,
and
mea
sure
s of
mon
ey s
uppl
y.
(con
tinu
ed)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 55
Icel
and
Indi
a
Indo
nesi
a
Ital
y
Tab
le A
1.
Mai
n D
iffe
renc
es b
etw
een
Mad
diso
n’s
GD
P D
ata
and
Dat
a U
sed
in T
his
Pape
r (C
onti
nued
)
Cou
ntry
Foc
us p
erio
dM
addi
son
(upd
ated
ver
sion
)O
ur a
ppro
ach
Wor
ld W
ar I
I(1
938–
50)
19th
–20t
hce
ntur
ies
19th
cen
tury
Wor
ld W
ar I
I(1
942–
48)
19th
–20t
hce
ntur
ies
Mis
mat
ch w
ith
indi
cate
dso
urce
, whi
ch s
eem
s to
cont
ain
only
ben
chm
ark
valu
es f
or 1
938
and
1947
;es
tim
atio
n pr
oced
ure
for
the
year
s in
bet
wee
n is
undi
sclo
sed.
Not
con
side
red
sepa
rate
ly b
utas
par
t of
an a
ggre
gate
of
coun
trie
s w
hose
pre
-195
0gr
owth
rat
es a
re a
ssum
ed
to e
qual
the
aver
ages
of
larg
er W
este
rn E
urop
ean
coun
trie
s.P
rese
nts
cont
inuo
us s
erie
sst
arti
ng in
188
4.M
issi
ng fi
gure
s.
Use
s pr
evio
us e
stim
ates
bas
edon
old
er o
ffici
al s
tati
stic
alse
ries
.
Est
imat
ed v
alue
s be
twee
n th
e tw
o be
nchm
ark
year
s by
app
ropr
iate
ly w
eigh
ting
data
on
indu
stri
al p
rodu
ctio
n an
d ag
ricu
ltur
al p
rodu
ctio
n (i
nclu
ding
cro
psan
d an
imal
s), w
hich
wer
e ca
libr
ated
to m
atch
the
obse
rved
evo
luti
on o
fag
greg
ate
GD
P d
urin
g ov
erla
ppin
g ye
ars.
Abs
olut
e la
ck o
f da
ta d
oes
not
allo
w b
uild
ing
an e
stim
ate
for
1944
.
Con
side
red
as a
sep
arat
e co
untr
y; c
ombi
ned
sour
ces
to c
onst
ruct
a c
onti
nuou
sse
ries
sta
rtin
g in
187
0.
Con
stru
cted
a d
iffe
rent
ser
ies
com
bini
ng v
ario
us s
ourc
es th
at a
llow
sta
rtin
g in
1872
.B
uilt
estim
ates
fol
low
ing
an in
dica
tors
app
roac
h ba
sed
on w
eigh
ted
mov
emen
tsin
the
foll
owin
g se
ctor
s: f
ood
and
crop
s, m
inin
g, c
onst
ruct
ion
and
hous
ing,
trad
e an
d se
rvic
es, p
ubli
c ad
min
istr
atio
n, a
nd o
il a
nd g
as. E
stim
ates
wer
eco
nstr
aine
d to
mat
ch a
ctua
l GD
P g
row
th r
ates
for
sur
roun
ding
yea
rs.
Con
stru
cted
a s
erie
s w
ith
the
sam
e st
arti
ng d
ate
but a
dif
fere
nt c
ombi
nati
on o
fso
urce
s, s
ome
of w
hich
are
rec
ent r
evis
ions
of
the
olde
r st
atis
tica
l figu
res
used
in M
addi
son’
s se
ries
and
are
sup
port
ed in
ric
her
esti
mat
es o
f in
dust
ry,
agri
cult
ure,
and
ser
vice
s.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 56
Japa
n
Mal
aysi
a
Mex
ico
Net
herl
ands
Sin
gapo
re
Wor
ld W
ar I
I(1
945)
20th
cen
tury
Rev
olut
ion
peri
od(1
911–
20)
1896
–99
19th
–20t
hce
ntur
ies
(Wor
ld W
ars
I an
d II
)
Ear
ly 2
0th
cent
ury
App
aren
tly,
194
5 va
lue
isas
sum
ed to
be
half
of
1944
.S
erie
s st
arts
in 1
911,
mis
sing
1943
–46.
Ter
rito
rial
adju
stm
ent t
o fi
t figu
res
topr
esen
t-da
y M
alay
sia.
Use
s li
near
inte
rpol
atio
n as
done
in a
noth
er s
ourc
e.
Mis
sing
.S
tart
s co
ntin
uous
ser
ies
in18
20; c
over
s w
ar y
ears
wit
hun
disc
lose
d ag
greg
ate
mea
sure
s.
Con
tinu
ous
seri
es s
tart
s in
1950
. Ben
chm
ark
for
1913
is p
rovi
ded,
app
aren
tly
base
d on
the
assu
mpt
ion
that
per
capi
ta G
DP
mov
edpr
opor
tion
atel
y to
that
of
Mal
aysi
a.
Use
d th
e m
ore
rece
nt c
onse
nsus
figu
res
show
ing
a de
clin
e in
out
put o
fap
prox
imat
ely
50 p
erce
nt s
prea
d ov
er b
oth
1945
and
194
6.E
xten
ded
the
seri
es b
ack
to 1
900
usin
g re
cent
ly p
ubli
shed
rev
isio
ns o
f ol
der
seri
es c
orre
spon
ding
to M
alay
a.
Con
stru
cted
est
imat
es b
ased
on
wei
ghte
d ch
ange
s in
ser
vice
s, a
gric
ultu
re, a
ndin
dust
ry (
incl
udin
g m
inin
g, e
nerg
y, a
nd m
anuf
actu
ring
). F
or e
ach
of th
ese
sect
ors,
we
buil
t sub
sect
or-w
eigh
ted
inde
xes
usin
g an
arr
ay o
f da
ta f
rom
nati
onal
sta
tist
ical
abs
trac
ts a
nd v
ario
us a
cade
mic
wor
ks o
n th
e re
volu
tion
.(M
addi
son’
s po
pula
tion
ser
ies
is a
line
ar in
terp
olat
ion
betw
een
1910
and
1920
, a p
roce
dure
that
yie
lds
inco
rrec
t mea
sure
s of
per
cap
ita
outp
ut. W
eus
ed a
pop
ulat
ion
seri
es th
at a
ccor
ds w
ith
the
mor
e li
kely
dem
ogra
phic
chan
ges
duri
ng th
is p
erio
d.)
Cov
ered
wit
h of
fici
al G
DP
figu
res.
Con
stru
cted
new
ser
ies
wit
h th
e pu
rpos
e of
ext
endi
ng th
e se
ries
fur
ther
bac
kin
to th
e pa
st, b
eing
exp
lici
t abo
ut p
roxi
es u
sed
as m
easu
res
of G
DP
, and
taki
ng a
dvan
tage
of
new
rev
isio
ns to
old
er s
erie
s. I
n pa
rtic
ular
, defl
ated
mea
sure
s of
gro
ss d
omes
tic
inco
me
wer
e us
ed to
ext
end
the
seri
es to
the
earl
y ye
ars
of th
e 19
th c
entu
ry. I
n th
e ab
senc
e of
a G
DP
agg
rega
te, w
orld
war
yea
rs w
ere
cove
red
wit
h fi
gure
s co
rres
pond
ing
to n
et n
atio
nal p
rodu
ct.
Use
d ne
wly
gen
erat
ed s
erie
s of
GD
P s
tart
ing
in 1
900
(but
mis
sing
the
peri
od19
40–4
9), b
ased
on
esti
mat
ion
of a
ll d
eman
d-si
de c
ompo
nent
s of
GD
P.
(con
tinu
ed)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 57
Sou
thA
fric
aS
outh
K
orea
Sw
eden
Sw
itze
rlan
d
20th
cen
tury
Ear
ly 1
9th
cent
ury
and
war
per
iods
(194
1–53
)
19th
–20t
hce
ntur
ies
Wor
ld W
ar I
to19
20s
(191
4–29
)
Pre
sent
s da
ta s
tart
ing
in 1
950.
Old
er e
stim
ates
; mis
mat
ches
wit
h in
dica
ted
sour
ces
for
the
war
yea
rs; u
ndis
clos
edes
tim
atio
n pr
oced
ure.
Sou
rce
from
an
olde
r st
udy;
seri
es s
tart
s in
182
0.U
ses
a ba
seli
ne s
ourc
e th
atpr
oxie
s ou
tput
wit
h m
ovin
gav
erag
es o
f ra
ilro
adtr
ansp
ort v
olum
e fo
r19
14–2
4 (c
ombi
ned
wit
hin
dust
rial
pro
duct
ion
for
1925
–29)
. Adj
ustm
ents
tom
atch
mov
emen
ts in
ano
ther
sour
ce a
re n
ot d
etai
led.
Ext
ende
d th
e se
ries
bac
k to
191
1.
Use
d re
sult
s fr
om r
ecen
t res
earc
h to
cov
er th
e fi
rst h
alf
of th
e 20
th c
entu
ry.
Con
stru
cted
est
imat
es f
or W
orld
War
II
peri
od b
ased
on
sect
oral
out
put i
nag
ricu
ltur
e, f
ores
try,
fish
ery,
min
ing,
man
ufac
turi
ng, a
nd s
ervi
ces.
Wei
ghte
din
dexe
s fo
r ea
ch o
f th
ese
subs
ecto
rs w
ere
cons
truc
ted
mai
nly
from
pri
mar
yK
orea
n st
atis
tica
l abs
trac
ts. F
or th
e K
orea
n W
ar y
ears
, we
used
sta
tist
ical
data
fro
m th
e U
nite
d N
atio
ns.
Ext
ende
d th
e se
ries
bac
k to
180
0 us
ing
rece
ntly
pub
lish
ed fi
gure
s co
mpa
tibl
ew
ith
revi
sed
offi
cial
dat
a an
d co
veri
ng th
e tw
o ce
ntur
ies.
Ree
stim
ated
GD
P fi
gure
s fo
r th
is p
erio
d fo
llow
ing
an in
dica
tors
app
roac
hus
ing
a w
ider
set
of
vari
able
s: p
riva
te c
onsu
mpt
ion
(in
turn
est
imat
ed f
or
1851
–194
8 fr
om q
uant
itie
s of
con
sum
ptio
n it
ems
and
expe
ndit
ure
shar
es),
expe
ndit
ures
of
the
conf
eder
atio
n, e
xpor
ts, i
mpo
rts,
fre
ight
traf
fic
onra
ilw
ays,
gro
ss c
onsu
mpt
ion
of e
nerg
y, in
dust
rial
pro
duct
ion,
num
ber
ofne
w r
esid
ence
s, n
umbe
r of
sto
ck c
ompa
nies
, and
cap
ital
at y
ear
end
of s
tock
com
pani
es. W
hene
ver
nece
ssar
y, a
con
sum
er p
rice
inde
x (b
uilt
for
pur
pose
sof
the
priv
ate
cons
umpt
ion
seri
es)
was
use
d as
defl
ator
.
Tab
le A
1.
Mai
n D
iffe
renc
es b
etw
een
Mad
diso
n’s
GD
P D
ata
and
Dat
a U
sed
in T
his
Pape
r (C
onti
nued
)
Cou
ntry
Foc
us p
erio
dM
addi
son
(upd
ated
ver
sion
)O
ur a
ppro
ach
11302-04_Barro.qxd 8/15/08 5:38 PM Page 58
Tai
wan
Uni
ted
Kin
gdom
Uni
ted
Sta
tes
Ven
ezue
la
Sour
ces:
Mad
diso
n (2
003)
and
Int
erne
t up
date
s (w
ww
.ggd
c.ne
t/mad
diso
n) t
hrou
gh M
ay 2
008;
for
det
ails
on
our
sour
ces
and
proc
edur
es s
ee t
he o
nlin
e ap
pend
ix a
tw
ww
.eco
nom
ics.
harv
ard.
edu/
facu
lty/b
arro
/dat
a_se
ts_b
arro
19th
–20t
hce
ntur
ies
War
per
iods
(193
9–49
)
19th
–20t
hce
ntur
ies
19th
–20t
hce
ntur
ies
19th
cen
tury
(188
4–99
)
Adj
ustm
ents
bas
ed o
n a
com
bina
tion
of
sour
ces,
not
full
y ex
plai
ned.
Cov
ers
1939
–45
wit
h ol
der
esti
mat
es a
nd 1
945–
49 b
yas
sum
ing
equa
l per
cent
age
grow
th f
or e
ach
of th
ese
year
s.U
ses
vari
ous
sour
ces;
mak
esas
sum
ptio
ns r
elat
ed to
terr
itor
ial a
djus
tmen
ts to
pres
ent-
day
boun
dari
es.
Pro
vide
s fi
ve b
ench
mar
kfi
gure
s fo
r 18
20–7
0.
Dis
card
s da
ta f
rom
the
sour
cefo
r pr
e-19
00 d
ecad
es.
Pre
ferr
ed to
con
stru
ct a
new
ser
ies
acco
unti
ng f
or s
peci
fic
deta
ils,
for
exa
mpl
e,th
e us
e of
an
actu
al G
DP
defl
ator
, ava
ilab
le f
or th
e ea
rlie
r pa
rt o
f th
e se
ries
star
ting
in 1
851,
and
the
use
of n
et n
atio
nal p
rodu
ct to
cov
er th
e la
ck o
f a
GD
P m
easu
re d
urin
g 19
30–4
8.U
sed
rece
ntly
pub
lish
ed s
erie
s ba
sed
on r
evis
ed n
atio
nal a
ccou
nts
stat
isti
cs f
orth
e 20
th c
entu
ry. T
his
new
sou
rce
pres
ents
con
stan
t pri
ce s
erie
s ba
sed
ondi
ffer
ent d
eflat
ing
met
hods
, all
of
whi
ch s
how
dif
fere
nt p
atte
rns
than
old
eres
tim
ates
.
Alt
houg
h pa
tter
ns d
o no
t cha
nge
mar
kedl
y, w
e ch
ose
a di
ffer
ent c
onca
tena
tion
of s
ourc
es. S
ome
of th
ese
are
them
selv
es “
com
prom
ise”
ser
ies
of e
arli
eres
tim
ates
; offi
cial
sou
rces
for
pos
t-W
orld
War
II
data
.
Res
tric
ted
the
seri
es to
sta
rt in
186
9 w
ith
the
esti
mat
es f
rom
Bal
ke a
nd G
ordo
n(1
989)
thro
ugh
1929
; fol
low
ed b
y N
atio
nal I
ncom
e an
d P
rodu
ct A
ccou
nts
figu
res
from
the
Bur
eau
of E
cono
mic
Ana
lysi
s up
to 2
006.
Alt
houg
hes
tim
ates
for
ear
lier
yea
rs a
re a
vail
able
fro
m a
new
edi
tion
of
the
His
tori
cal
Stat
isti
cs o
f the
Uni
ted
Stat
es,w
e be
liev
e th
ese
figu
res
war
rant
fur
ther
anal
ysis
, esp
ecia
lly
thos
e co
rres
pond
ing
to th
e C
ivil
War
per
iod.
Sta
rted
the
seri
es in
188
4 us
ing
GD
P e
stim
ates
bas
ed o
n a
wid
e co
vera
ge o
fse
ctor
s, in
clud
ing
agri
cult
ure,
com
mer
ce, fi
nanc
es, g
over
nmen
t, an
dtr
ansp
orts
.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 59
60 Brookings Papers on Economic Activity, Spring 2008
A P P E N D I X B
Real Consumption and GDP per Capita by Country
Figure B1. Real Personal Consumer Expenditure and GDP per Capita in OECD Countries
6
7
8
9
10
1880 1900 1920 1940 1960 1980 2000
GDP
C
AustraliaLog of C or GDP
6
7
8
9
10
1880 1900 1920 1940 1960 1980 2000
GDP
C
CanadaLog of C or GDP
6
7
8
9
10
1880 1900 1920 1940 1960 1980 2000
GDP
C
BelgiumLog of C or GDP
6
7
8
9
10
1880 1900 1920 1940 1960 1980 2000
GDP
C
DenmarkLog of C or GDP
6
7
8
9
10
1880 1900 1920 1940 1960 1980 2000
GDP
C
FinlandLog of C or GDP
6
7
8
9
10
1880 1900 1920 1940 1960 1980 2000
GDP
C
FranceLog of C or GDP
11302-04_Barro.qxd 8/15/08 5:38 PM Page 60
ROBERT J. BARRO and JOSÉ F. URSÚA 61
6
7
8
9
10
1880 1900 1920 1940 1960 1980 2000
GDP
C
Log of C or GDP
6
7
8
9
10
Log of C or GDP
6
7
8
9
10
1880
Log of C or GDP
6
7
8
9
10
Log of C or GDP
6
7
8
9
10
Log of C or GDP
6
7
8
9
10
Log of C or GDP
1880 1900 1920 1940 1960 1980 2000
1900 1920 1940 1960 1980 2000 1880 1900 1920 1940 1960 1980 2000
1880 1900 1920 1940 1960 1980 2000
1880 1900 1920 1940 1960 1980 2000
GDP
C
GDP
C
GDP
C
C
GDP
C
GDP
Germany
Japan
Italy
Netherlands
Norway Portugal
Figure B1. Real Personal Consumer Expenditure and GDP per Capita in OECD Countries (Continued)
(continued)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 61
62 Brookings Papers on Economic Activity, Spring 2008
6
7
8
9
10
1880 1900 1920 1940 1960 1980 2000
GDP
C
Log of C or GDP
6
7
8
9
10
Log of C or GDP
6
7
8
9
10
1880
Log of C or GDP
6
7
8
9
10
Log of C or GDP
6
7
8
9
10
Log of C or GDP
1880 1900 1920 1940 1960 1980 2000
1900 1920 1940 1960 1980 2000
1880 1900 1920 1940 1960 1980 2000
1880 1900 1920 1940 1960 1980 2000
GDP
C
GDP
C
GDP
C
C
GDP
Spain
Switzerland
Sweden
United Kingdom
United States
Source: ???a. Log scale ranges from 5.5 to 11.0 ($245 to $59,900, respectively, in 2000 U.S. dollars). Series start
in 1869 or later depending on data availability.
Figure B1. Real Personal Consumer Expenditure and GDP per Capita in OECD Countries (Continued)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 62
ROBERT J. BARRO and JOSÉ F. URSÚA 63
Figure B2. Real Personal Consumer Expenditure and GDP per Capita in Non-OECD Countries
6
7
8
9
10
1880 1900 1920 1940 1960 1980 2000
GDP
C
Log of C or GDP
6
7
8
9
10
Log of C or GDP
6
7
8
9
10
Log of C or GDP
6
7
8
9
10
Log of C or GDP
1880 1900 1920 1940 1960 1980 2000
1880 1900 1920 1940 1960 1980 2000
1880 1900 1920 1940 1960 1980 2000
GDP
C
GDP
C
GDP
C
Argentina
Chile
Brazil
Mexico
(continued)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 63
64 Brookings Papers on Economic Activity, Spring 2008
Figure B2. Real Personal Consumer Expenditure and GDP per Capita in Non-OECD Countries (Continued)
6
7
8
9
10
1880 1900 1920 1940 1960 1980 2000
GDP
C
Log of C or GDP
6
7
8
9
10
1880
Log of C or GDP
6
7
8
9
10
Log of C or GDP
1900 1920 1940 1960 1980 2000
1880 1900 1920 1940 1960 1980 2000
GDP
C
C
GDP
Peru South Korea
Taiwan
Source: ???a. Log scale ranges from 5.5 to 11.0 ($245 to $59,900, respectively, in 2000 U.S. dollars). Series start
in 1869 or later depending on data availability.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 64
ROBERT J. BARRO and JOSÉ F. URSÚA 65
A P P E N D I X C
Characteristics of Consumption and GDP Disasters
Table C1. Consumption Disasters
Decline in consumer Stock- Rate of
expenditure price return Inflation Country Trougha Peak per capitab declinec on billsd rated
OECD countriesAustralia 1918 1913 0.238 0.144 −0.008 0.036
1932 1927 0.234 0.069 0.086 −0.0321944 1938 0.301 0.225 −0.024 0.041
Austriae 1918 1913 0.451 — 0.034 0.0191933 1929 0.217 0.533 0.071 −0.0041947 1938 0.438? — — —
Belgium 1917 1913 0.445 — −0.160 0.3531942 1937 0.530 −0.024 0.034
Canada 1876 1873 0.152 — — −0.0231908 1906 0.113 — 0.014 −0.0461915 1912 0.130 — 0.022f 0.0341921 1918 0.196 0.210 — 0.1041933 1929 0.230 0.650 — −0.054
Denmark 1921 1919 0.241 0.502 −0.113 0.2011941 1939 0.261 0.336 −0.120 0.1931948 1946 0.144 0.040 0.005 0.025
Finland 1892 1890 0.102 — — —1918 1913 0.360 — −0.194g 0.389g
1932 1928 0.199 0.207 0.115 −0.0411944 1938 0.254 0.168 −0.067 0.1221993 1989 0.140 0.620 0.092 0.045
France 1871 1864 0.158 0.212 0.027 0.0071915 1912 0.215 0.171 0.031 0.0061943 1938 0.580 — −0.121 0.162
Germany 1918 1912 0.425 0.539 −0.101 0.1861923 1922 0.127 0.654 −0.970 34.51932 1928 0.121 0.562 0.109 −0.0351945 1939 0.412 −0.366 0.000 0.020
Greecee 1944 1938 0.636 0.442h −0.442 4.651946 1945 0.113 — — —
Icelande 1952 1947 0.250 — — 0.2021969 1967 0.118 — — 0.1081975 1974 0.107 — — 0.5151993 1987 0.176 — 0.060i 0.144
Italy 1945 1939 0.286 0.429 −0.236 1.02Japan 1945 1937 0.639 0.457 −0.066 0.101Netherlands 1893 1889 0.098 — −0.013 0.038
1918 1912 0.440 — −0.013 0.0601944 1939 0.545 −0.506 −0.050 0.069
New Zealande 1944 1939 0.224 0.089 −0.009 0.031
Disaster period
(continued)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 65
66 Brookings Papers on Economic Activity, Spring 2008
Table C1. Consumption Disasters (Continued)
Decline in consumer Stock- Rate of
expenditure price return Inflation Country Trougha Peak per capitab declinec on billsd rated
Disaster period
Norway 1918 1916 0.169 −0.035 −0.212 0.3261921 1919 0.161 0.536 −0.032 0.0941944 1939 0.100 −0.222 −0.062 0.090
Portugal 1919 1913 0.215 — — —1936 1934 0.121 −0.434 0.044 0.0101942 1939 0.104 0.084 −0.058 0.1101976 1974 0.098 — −0.136 0.242
Spain 1896 1892 0.182 −0.088 0.079 −0.0241915 1913 0.128 0.065 0.021 0.0261930 1929 0.101 0.090 0.027 0.0281937 1935 0.461 0.238j −0.051 0.0581945 1940 0.145 −0.079 −0.021 0.1071949 1946 0.131 0.014 −0.029 0.075
Sweden 1917 1913 0.115 0.095 −0.014 0.0741921 1920 0.132 0.251 0.052 0.0191945 1939 0.182 0.173 −0.030 0.059
Switzerland 1872 1870 0.190 — — —1878 1876 0.225 — — —1883 1881 0.142 — — −0.0181886 1885 0.141 — — −0.0591888 1887 0.157 — — 0.0101918 1912 0.108 0.475 −0.031 0.0881945 1939 0.173 0.382 −0.052 0.074
United Kingdom 1918 1915 0.167 0.490 −0.117 0.1881943 1938 0.169 0.123 −0.032 0.047
United States 1921 1917 0.164 0.584 −0.071 0.1391933 1929 0.208 0.631 0.093 −0.064
Non-OECD countriesArgentina 1891 1887 0.123 — — 0.080
1898 1895 0.283 — — 0.0301900 1899 0.195 — — −0.0961902 1901 0.127 — — 0.0591907 1906 0.123 — — 0.0251917 1912 0.172 — — 0.0471932 1928 0.189 — — −0.0281959 1958 0.101 — — 0.5071982 1980 0.104 0.575 0.516 1.091990 1987 0.160 −3.264 −0.249 18.32002 1998 0.249 0.401 0.090 −0.009
Brazil 1905 1902 0.148 — — −0.0291909 1906 0.157 — — 0.0231919 1918 0.109 — — 0.1231921 1920 0.147 — — 0.0991931 1928 0.201 — — −0.0371990 1984 0.163 −0.271 — 6.42
11302-04_Barro.qxd 8/15/08 5:38 PM Page 66
ROBERT J. BARRO and JOSÉ F. URSÚA 67
Chile 1915 1911 0.322 0.125 0.021 0.0691922 1918 0.181 0.154 0.011 0.0851932 1929 0.374 0.538 0.063 0.0071956 1954 0.136 −0.315 −0.410 0.7751976 1972 0.401 −2.470 −0.516 3.471985 1981 0.327 0.684 0.165 0.191
Colombiae 1932 1929 0.181 0.263 — −0.0901943 1939 0.228 −0.053 — 0.0411999 1997 0.099 0.043 0.095 0.172
Indiae 1942 1932 0.217 −0.814 0.003 0.0161946 1943 0.130 −0.305 −0.053 0.0861950 1947 0.177 0.504 −0.025 0.038
Malaysiae 1916 1914 0.096 — — —1920 1917 0.425 — — —1932 1929 0.258 — — —1947? 1938 0.336? — — —1952 1951 0.118 — — 0.1641986 1984 0.145 0.434 0.036 0.0141998 1997 0.124 0.533 0.036 0.029
Mexico 1916 1909 0.252 — — 0.031k
1924 1921 0.118 — — −0.0741932 1926 0.311 0.406m — −0.0251988 1981 0.161 −0.148 0.024 0.8521995 1994 0.113 0.147 0.075 0.071
Peru 1914 1907 0.118 — — —1932 1929 0.140 0.105 — −0.0431979 1975 0.179 0.325 — 0.4371992 1987 0.300 0.519 −0.522 24.8
Singaporee 1916 1910 0.145 — — —1920 1918 0.127 — — —1931 1928 0.104 — — —1951 1949 0.159 — — 0.0981959 1956 0.117 — — 0.013
South Korea 1945 1942 0.387 — — —1952 1949 0.371 — — 1.681998 1997 0.143 0.458 0.072 0.066
Taiwan 1905 1903 0.219 — — 0.0761911 1910 0.127 — — 0.0821945 1936 0.684 — — 0.148
Turkeye 1932 1929 0.120 — — −0.0311946 1938 0.298 — — 0.2152001 2000 0.108 0.565 −0.078 0.390
Uruguaye 1965 1960 0.099 — — 0.2741984 1981 0.267 — — 0.3382002 1998 0.219 — — 0.054
Table C1. Consumption Disasters (Continued)
Decline in consumer Stock- Rate of
expenditure price return Inflation Country Trougha Peak per capitab declinec on billsd rated
Disaster period
(continued)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 67
68 Brookings Papers on Economic Activity, Spring 2008
Venezuelae 1933 1930 0.311 0.074 — −0.0601936 1935 0.107 −0.069 — −0.0581952 1948 0.203 0.103 −0.025 0.0481964 1957 0.223 0.329 0.020 0.0161989 1982 0.320 −3.493 −0.048 0.1832003 1993 0.147 0.690 −0.043 0.421
Source: Authors’ construction; for details on sources and procedures see the online appendix atwww.economics.harvard.edu/faculty/barro/data_sets_barro.
a. Italics indicate that the country was a current participant in an external or internal war.b. Decline in real personal consumer expenditure per capita by 0.1 or greater, expressed as a cumula-
tive fraction from peak year to trough year.c. Decline in real stock prices, expressed as cumulative fractions from the end of the year preceding the
peak to the end of the year preceding the trough (unless the timing is indicated otherwise because ofmissing data). Negative numbers indicate increases in real stock prices.
d. Mean values from the peak year to one year before the trough year (unless the timing is indicatedotherwise because of missing data).
e. Not included in the analysis for the consumer expenditure sample.f. 1913–14. g. 1915–17. h. 1937–40. i. 1988–92 j. 1934–35. k. 1909–13. m. 1929–31.
Table C1. Consumption Disasters (Continued)
Decline in consumer Stock- Rate of
expenditure price return Inflation Country Trougha Peak per capitab declinec on billsd rated
Disaster period
11302-04_Barro.qxd 8/15/08 5:38 PM Page 68
ROBERT J. BARRO and JOSÉ F. URSÚA 69
Table C2. GDP Disasters
Decline in Stock- Rate ofGDP per price return Inflation
Country Trougha Peak capitab declinec on billsd rated
OECD countriesAustralia 1895 1889 0.271 0.067 0.085 −0.050
1918 1910 0.118 0.188 −0.020 0.0451931 1926 0.221 0.179 0.061 −0.0131946 1943 0.145 −0.167 0.007 0.005
Austria 1918 1912 0.381 — 0.031 0.0221933 1929 0.235 0.533 0.071 −0.0041945 1941 0.587 — — —
Belgium 1918 1913 0.477 — −0.225 0.4921934 1930 0.117 0.451 0.070 −0.0521943 1937 0.453 −0.764 −0.033 0.045
Canada 1878 1874 0.117 — — −0.0201921 1917 0.301 0.393 — 0.1151933 1928 0.348 0.558 — −0.041
Denmark 1918 1914 0.160 0.132f −0.045 0.1281941 1939 0.239 0.336 −0.120 0.193
Finland 1881 1876 0.120 — — —1918 1913 0.353 — −0.194g 0.389g
1940 1938 0.103 0.142 0.017 0.0241993 1989 0.124 0.620 0.092 0.045
France 1870 1868 0.095 — — −0.0111879 1874 0.102 — — −0.0021886 1882 0.133 0.296 0.028 0.0001918 1912 0.289 0.395 −0.055 0.1171935 1929 0.187 0.535 0.068 −0.0391944 1939 0.414 — −0.147 0.197
Germany 1919 1913 0.357 0.736 −0.125 0.2141923 1922 0.135 0.654 −0.970 34.51932 1928 0.280 0.562 0.109 −0.0351946 1943 0.736 0.068 −0.009 0.028
Greece 1872 1868 0.106 — — —1877 1873 0.152 — — —1891 1888 0.233 — — —1897 1896 0.151 — — —1901 1899 0.144 — — —1913 1911 0.419 — — —1919 1918 0.177 — −0.553 1.381923 1921 0.238 — −0.203 0.3691942 1939 0.660 0.448h −0.331 4.31
Iceland 1883 1881 0.125 — — —1918 1913 0.221 — — 0.2061920 1919 0.157 — — 0.1141952 1948 0.139 — — 0.235
Italy 1920 1918 0.221 0.374 −0.101 0.1951945 1939 0.413 0.429 −0.236 1.02
Japan 1944 1940 0.503 0.239 −0.026 0.054
Disaster period
(continued)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 69
70 Brookings Papers on Economic Activity, Spring 2008
Table C2. GDP Disasters (Continued)
Decline in Stock- Rate ofGDP per price return Inflation
Country Trougha Peak capitab declinec on billsd rated
Disaster period
Netherlands 1918 1913 0.258 — −0.021 0.0701934 1929 0.129 0.582 0.057 −0.0321944 1939 0.525 −0.506 −0.050 0.069
New Zealand 1879 1878 0.174 — — —1909 1907 0.110 — — —1918 1911 0.107 — — 0.0401927 1925 0.117 — 0.057 0.0091948 1947 0.119 0.003 −0.061 0.0811951 1950 0.097 −0.049 −0.068 0.089
Norway 1918 1916 0.148 −0.035 −0.212 0.3261921 1920 0.110 0.447 −0.117 0.1941944 1939 0.193 −0.222 −0.062 0.090
Portugal 1928 1927 0.109 — — —1936 1934 0.148 −0.434 0.044 0.010
Spain 1896 1892 0.119 −0.088 0.079 −0.0241933 1929 0.096 0.464 0.061 −0.0091938 1935 0.313 0.238i −0.035 0.098
Sweden 1918 1916 0.150 0.169 −0.185 0.3231921 1920 0.108 0.251 0.052 0.0191941 1939 0.095 0.349 −0.071 0.104
Switzerland 1879 1875 0.161 — — —1918 1912 0.191 0.475 −0.031 0.0881942 1939 0.126 0.308 −0.080 0.105
United Kingdom 1921 1918 0.192 0.321 −0.069 0.1301947 1943 0.148 −0.269 0.003 0.006
United States 1908 1906 0.105 0.365 0.019 0.0411914 1913 0.095 0.160 0.034 0.0201921 1918 0.118 0.293 −0.057 0.1251933 1929 0.290 0.631 0.093 −0.0641947 1944 0.165 −0.061 −0.062 0.076
Non-OECD countriesArgentina 1891 1889 0.189 — — 0.284
1897 1896 0.219 — — 0.0691900 1899 0.147 — — −0.0961917 1912 0.289 — — 0.0471932 1929 0.195 — — −0.0021959 1958 0.101 — — 0.5071982 1980 0.111 0.575 0.516 1.091990 1988 0.141 −3.430 −0.355 26.62002 1998 0.220 0.401 0.090 −0.009
Brazil 1887 1884 0.105 — — −0.0201893 1891 0.262 — — 0.2481900 1895 0.135 — — 0.0331931 1928 0.201 — — −0.0371992 1987 0.110 0.358 — 10.8
11302-04_Barro.qxd 8/15/08 5:38 PM Page 70
ROBERT J. BARRO and JOSÉ F. URSÚA 71
Table C2. GDP Disasters (Continued)
Decline in Stock- Rate ofGDP per price return Inflation
Country Trougha Peak capitab declinec on billsd rated
Disaster period
Chile 1903 1902 0.111 0.015 0.022 0.0551915 1912 0.105 0.185 0.000 0.0901919 1918 0.126 −0.018 0.103 −0.0141932 1929 0.361 0.538 0.063 0.0071975 1971 0.240 −2.081 −0.479 2.671983 1981 0.180 0.499 0.296 0.151
Colombia NoneIndia 1877 1875 0.154 — — −0.065
1896 1894 0.100 — 0.120 −0.0601918 1916 0.146 — 0.004 −0.0611948 1943 0.117 0.073 −0.058 0.082
Indonesia 1933 1930 0.114 0.406 — −0.1861945 1940 0.545 — — 0.0441999 1997 0.158 0.681 −0.066 0.440
Malaysiae 1904 1902 0.100 — — —1935 1929 0.193 — — —1937 1936 0.117 — — —1941 1939 0.235 — — —1947? 1942 0.361 — — —
Mexico 1915 1909 0.119 — — 0.031j
1932 1926 0.314 0.406k — −0.0251988 1981 0.128 −0.148 0.024 0.852
Peru 1932 1929 0.258 0.105 — −0.0431979 1975 0.104 0.325 — 0.4371983 1981 0.136 0.879 — 0.7281992 1987 0.325 0.519 −0.522 24.8
Philippines 1904 1903 0.158 — — 0.2341915 1913 0.116 — — −0.1091935 1929 0.134 — — −0.0381946 1939 0.572 — — —1985 1982 0.187 0.736 −0.050 0.285
Singaporee 1904 1902 0.214 — — —1913 1910 0.337 — — —1916 1915 0.174 — — —1920 1917 0.235 — — —1927 1925 0.389 — — —1932 1929 0.412 — — —1938 1937 0.151 — — —1952 1950? 0.345 — — 0.1921957 1956 0.113 — — 0.033
South Africa 1917 1912 0.229 0.139 — 0.0311920 1919 0.239 −0.200 — 0.0091987 1981 0.113 −0.156 0.006 0.1471993 1989 0.102 0.028 0.032 0.140
South Korea 1919 1918 0.111 — — —1939 1938 0.104 — — —
(continued)
11302-04_Barro.qxd 8/15/08 5:38 PM Page 71
72 Brookings Papers on Economic Activity, Spring 2008
Table C2. GDP Disasters (Continued)
Decline in Stock- Rate ofGDP per price return Inflation
Country Trougha Peak capitab declinec on billsd rated
Disaster period
1945 1940 0.480 — — —1951 1949 0.151 — — 0.492
Sri Lanka 1878 1870 0.158 — — —1886 1883 0.141 — — —1923 1913 0.138 — — —1932 1929 0.147 — — —1946 1942 0.211 — — 0.147
Taiwan 1905 1903 0.214 — — 0.0761911 1910 0.114 — — 0.0821945 1936 0.662 — — 0.148
Turkeye 1927 1926 0.134 — — 0.0331932 1931 0.122 — — −0.0251945 1939 0.395 — — 0.283
Uruguay 1875 1872 0.269 — — —1881 1878 0.153 — — —1887 1886 0.140 — — −0.0541890 1888 0.202 — — 0.1811901 1896 0.156 — — 0.0451905 1904 0.122 — — −0.0811915 1912 0.280 — — 0.0571920 1919 0.142 — — 0.0991933 1930 0.367 — — −0.0051943 1939 0.139 — — 0.0331959 1957 0.118 — — 0.1901984 1981 0.236 — — 0.3382002 1998 0.186 — — 0.054
Venezuela 1892 1890 0.235 — — —1897 1893 0.225 — — —1907 1903 0.134 — — —1916 1913 0.167 — — 0.025m
1933 1930 0.162 0.074 — −0.0601942 1939 0.155 −0.134 — −0.0031961 1957 0.152 0.270 0.007 0.0201985 1977 0.295 0.616 −0.005 0.1212003 1993 0.259 0.690 −0.043 0.421
Source: Authors’ construction; for details on sources and procedures see the online appendix atwww.economics.harvard.edu/faculty/barro/data_sets_barro.
a. Italics indicate that the country was a current participant in an external or internal war.b. Decline in real GDP per capita by 0.1 or greater, expressed as a cumulative fraction from peak year
to trough year.c. Decline in real stock prices, expressed as a cumulative fractions from the end of the year preceding
the peak to the end of the year preceding the trough (unless the timing is indicated otherwise because ofmissing data). Negative numbers indicate increases in real stock prices.
d. Mean values from the peak year to one year before the trough year (unless the timing is indicatedotherwise because of missing data).
e. Not included in the analysis for the GDP sample.f. 1914–17. g. 1915–17. h. 1938–40. i. 1934–35. j. 1909–13. k. 1929–31. m. 1914–15.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 72
ROBERT J. BARRO and JOSÉ F. URSÚA 73
Table C3. Declines in Consumer Durables during Consumption Crisesa
Share of nominal durables Proportionate decline in nominal consumer in real consumer
expenditure per capita expenditure per capita
Consumer Nondurables Country Year Share Year Share expenditureb Durables and services
OECD countriesCanada 1933 0.054 1929 0.085 0.230 0.507 0.201Finland 1892 0.029 1890 0.042 0.102 0.132 0.101
1918 0.010 1913 0.017 0.360 0.655 0.3531932 0.013 1928 0.030 0.199 0.636 0.1821944 0.019 1938 0.038 0.254 0.634 0.2371993 0.072 1989 0.138 0.140 0.512 0.062
Iceland 1969 0.101 1967 0.133 0.118 0.321 0.0871975 0.134 1974 0.181 0.107 0.340 0.0431993 0.102 1987 0.183 0.176 0.529 0.053
Portugal 1976 0.092 1974 0.101 0.098 0.195 0.091Spain 1896 0.020 1892 0.018 0.182 0.063 0.185
1915 0.020 1913 0.034 0.128 0.405 0.1091930 0.045 1929 0.057 0.101 0.238 0.0901937 0.022 1935 0.034 0.461 0.642 0.4501945 0.023 1940 0.019 0.145 −0.206 0.1531949 0.025 1946 0.027 0.131 0.170 0.127
United 1918 0.040 1915 0.037 0.167 0.198 0.166Kingdom 1943 0.023 1938 0.049 0.169 0.649 0.144
United 1921 0.094 1917 0.094 0.164 0.227 0.158States 1933 0.076 1929 0.119 0.208 0.501 0.169
Non-OECD countriesChile 1985 0.060 1981 0.098 0.327 0.695 0.179Colombia 1999 0.088 1997 0.110 0.099 0.314 0.060Mexico 1995 0.070 1994 0.082 0.113 0.340 0.077South Korea 1998 0.063 1997 0.089 0.143 0.363 0.096Turkey 2001 0.150 2000 0.195 0.108 0.315 0.056Venezuela 1964 0.042 1957 0.079 0.223 0.581 0.184
1989 0.047 1982 0.073 0.320 0.643 0.2992003 0.076 1993 0.081 0.147 0.478 0.105
Overall means 0.058 0.080 0.183 0.396 0.151
a. This table shows the universe of consumption crises considered in table C1 for which we have been able tobreak down the decline in real personal consumer expenditure per capita into durables, on the one hand, and non-durables and services, on the other. The latter category should be closer to “consumption.” Of the twenty-eightconsumer expenditure crises for which the necessary data are available, twenty are included in our main sampleof ninety-five crises in table C1.
b. From table C1.
Trough Peak
11302-04_Barro.qxd 8/15/08 5:38 PM Page 73
74 Brookings Papers on Economic Activity, Spring 2008
Table C4. Consumption Disasters Gauged by One-Sided Hodrick-Prescott Filtersa
Decline in real personal consumer
Country Troughb Peak expenditure per capita
OECD countriesAustralia 1920 1913 0.202
1935 1928 0.1671945 1938 0.215
Belgium 1944 1938 0.505Canada 1923 1913 0.166
1935 1930 0.136Denmark 1943 1939 0.202Finland 1919 1913 0.201
1933 1929 0.1051944 1939 0.181
France 1874 1864 0.1041918 1913 0.1851944 1934 0.530
Germany 1920 1913 0.3841947 1940 0.356
Icelandc 1995 1988 0.096Italy 1946 1940 0.221Japan 1936 1928 0.123
1946 1937 0.515Netherlands 1919 1913 0.264
1944 1934 0.487Norway NonePortugal NoneSpain 1939 1929 0.416Sweden 1945 1940 0.106Switzerland 1945 1940 0.142U.K. 1918 1915 0.109
1944 1939 0.160U.S. 1934 1929 0.136
Non-OECD countriesArgentina 1933 1929 0.141
1990 1980 0.1682004 2000 0.149
Brazil 1992 1985 0.158Chile 1917 1913 0.198
1933 1930 0.2471978 1973 0.3201987 1981 0.157
Colombiac 1945 1941 0.095Indiac 1942 1933 0.184Malaysiac 1922 1917 0.297
1934 1930 0.141
Disaster period
11302-04_Barro.qxd 8/15/08 5:38 PM Page 74
ROBERT J. BARRO and JOSÉ F. URSÚA 75
Mexico 1916 1909 0.1941934 1926 0.2401988 1982 0.115
Peru 1914 1909 0.0951985 1976 0.2051993 1988 0.229
Singaporec 1916 1910 0.103South Korea 1947 1942 0.325
1952 1949 0.127Taiwan 1947 1937 0.578Turkeyc 1946 1940 0.222Uruguayc 1985 1981 0.189
2004 2000 0.134Venezuelac 1933 1930 0.499
1971 1961 0.1481990 1982 0.331
Source: Authors’ construction; for details on sources and procedures see the online appendix atwww.economics.harvard.edu/faculty/barro/data_sets_barro.
a. Analysis is based on one-sided Hodrick-Prescott filters for the logarithm of real consumer expendi-ture per capita, using a conventional smoothing parameter of 100. Declines are expressed as cumulativefractions from peak year to trough year.
b. Italics indicate that the country was a current participant in an external or internal war.c. Not included in the analysis for the consumer expenditure sample.
Table C4. Consumption Disasters Gauged by One-Sided Hodrick-Prescott Filtersa (Continued)
Decline in real personal consumer
Country Troughb Peak expenditure per capita
Disaster period
11302-04_Barro.qxd 8/15/08 5:38 PM Page 75
76 Brookings Papers on Economic Activity, Spring 2008
Table C5. GDP Disasters Gauged by One-Sided Hodrick-Prescott Filters
Decline in realCountry Trough Peak GDP per capita
Australia 1897 1891 0.2551920 1913 0.1091933 1928 0.163
Austria 1920 1913 0.3461936 1930 0.2261947 1943 0.455
Belgium 1919 1913 0.4361935 1930 0.1081945 1938 0.426
Canada 1922 1917 0.1911935 1930 0.250
Denmark 1943 1939 0.165Finland 1919 1914 0.225France 1919 1913 0.208
1938 1930 0.1801945 1939 0.310
Germany 1920 1913 0.3211933 1929 0.1721949 1944 0.663
Greece 1872 1862 0.2001898 1888 0.1741917 1912 0.2601945 1939 0.626
Iceland 1921 1915 0.189Italy 1946 1940 0.267Japan 1949 1943 0.439Netherlands 1919 1914 0.174
1935 1930 0.1281945 1939 0.426
New Zealand 1888 1879 0.1161933 1925 0.125
Norway 1945 1939 0.115Portugal NoneSpain 1939 1930 0.316Sweden 1921 1916 0.131Switzerland 1883 1876 0.110
1919 1912 0.1321944 1934 0.127
United Kingdom 1923 1918 0.1431949 1944 0.109
United States 1934 1929 0.221
Non-OECD countriesArgentina 1918 1912 0.248
1934 1929 0.1351990 1980 0.2012003 1999 0.113
Disaster period
11302-04_Barro.qxd 8/15/08 5:38 PM Page 76
ROBERT J. BARRO and JOSÉ F. URSÚA 77
Table C5. GDP Disasters Gauged by One-Sided Hodrick-Prescott Filters (Continued)
Decline in realCountry Trough Peak GDP per capita
Disaster period
Brazil 1900 1891 0.175Chile 1933 1930 0.201
1977 1972 0.170India 1950 1943 0.103Indonesia 1947 1941 0.517Malaysiac 1941 1931 0.184Mexico 1915 1910 0.105
1934 1926 0.243Peru 1933 1929 0.137
1985 1976 0.1421993 1987 0.269
Philippines 1988 1983 0.171Singaporec 1916 1911 0.212
1928 1925 0.1531932 1930 0.178
South Africa 1994 1984 0.156South Korea 1952 1942 0.486Sri Lanka 1923 1914 0.107Taiwan 1947 1938 0.594Turkeyc 1945 1940 0.276Uruguay 1901 1896 0.112
1917 1913 0.1761935 1930 0.2101967 1957 0.1691986 1981 0.1712003 2000 0.105
Venezuela 1901 1895 0.1091963 1958 0.1011989 1979 0.2982003 1993 0.157
Source: Authors’ construction; for details on sources and procedures see the online appendix atwww.economics.harvard.edu/faculty/barro/data_sets_barro.
a. Analysis is based on one-sided Hodrick-Prescott filters for the logarithm of real GDP per capita,using a conventional smoothing parameter of 100. Declines by 0.1 or greater are expressed as cumulativefractions from peak year to trough year.
b. Italics indicate that the country was a current participant in an external or internal war.c. Not included in the analysis for the consumer expenditure sample.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 77
78 Brookings Papers on Economic Activity, Spring 2008
A P P E N D I X D
Distributions of Disasters Using Hodrick-Prescott-Filtered Data
Figure D1. Distributions of Consumer Expenditure Disasters by Size and Duration,One-Sided HP-Filtereda
Source: Authors’ calculation; for details on sources and procedures see the online appendix at www.economics.harvard.edu/faculty/barro/data_sets_barro.
a. The sample is the forty-three personal consumption expenditure disasters listed in table C4 in appendix C.
3
6
7
No. of events
Cumulative fractional decline in HP-filtered C per capita
2
1
4
5
0.2 0.3 0.4 0.5 0.6
4
8
10
No. of events
Duration (years between trough and peak)
2
6
3 4 5 6 7 8 9 10
11302-04_Barro.qxd 8/15/08 5:38 PM Page 78
ROBERT J. BARRO and JOSÉ F. URSÚA 79
Figure D2. Distributions of GDP Disasters by Size and Duration, One-Sided HP-Filtereda
Source: Authors’ calculation; for details on sources and procedures see the online appendix at www.economics.harvard.edu/faculty/barro/data_sets_barro.
a. The sample is the seventy GDP disasters listed as in the sample in table C5 in appendix C.
12
No. of events
Cumulative fractional decline in HP-filtered C per capita
4
8
0.2 0.3 0.4 0.5 0.6
4
8
10
No. of events
Duration (years between trough and peak)
2
6
3 4 5 6 7 8 9 10
11302-04_Barro.qxd 8/15/08 5:38 PM Page 79
References
Balke, Nathan S., and Robert J. Gordon. 1989. “The Estimation of Prewar GrossNational Product: Methodology and New Evidence.” Journal of PoliticalEconomy 97, no. 1: 38–92.
Bansal, Ravi, and Amir Yaron. 2004. “Risks for the Long Run: A Potential Reso-lution of Asset-Pricing Puzzles.” Journal of Finance 59, no. 4: 1481–1509.
Barro, Robert J. 2006. “Rare Disasters and Asset Markets in the Twentieth Cen-tury.” Quarterly Journal of Economics 121, no. 3: 823–66.
———. 2008. Macroeconomics: A Modern Approach. Mason, Ohio: ThomsonSouth-Western.
———. Forthcoming. “Rare Disasters, Asset Prices, and Welfare Costs.” Ameri-can Economic Review.
Cagan, Phillip. 1965. Determinants and Effects of Changes in the Stock of Money,1875–1960. Columbia University Press.
Caselli, Francesco, and Jaume Ventura. 2000. “A Representative Consumer The-ory of Distribution.” American Economic Review 90, no. 4: 909–26.
Chatterjee, Satyajit, and Dean Corbae. 2007. “On the Aggregate Welfare Cost ofGreat Depression Unemployment.” Journal of Monetary Economics 54, no. 6:1529–44.
Cogley, Timothy. 1990. “International Evidence on the Size of the Random Walkin Output.” Journal of Political Economy 98, no. 3: 501–18.
Cogley, Timothy, and Thomas J. Sargent. 2008. “The Market Price of Risk and theEquity Premium: A Legacy of the Great Depression?” Journal of MonetaryEconomics 55, no. 3: 454–76.
Dimson, Elroy, Paul Marsh, and Mike Staunton. 2008. “The Worldwide EquityPremium: A Smaller Puzzle.” In Handbook of the Equity Risk Premium, editedby Rajnish Mehra. Amsterdam: Elsevier.
Epstein, Larry G., and Stanley E. Zin. 1989. “Substitution, Risk Aversion, and theTemporal Behavior of Consumption and Asset Returns: A Theoretical Frame-work.” Econometrica 57, no. 4: 937–69.
Fama, Eugene F. 1965. “The Behavior of Stock Market Prices.” Journal of Busi-ness 38, no. 1: 34–105.
Fujino, Shozaburo, and Ryoko Akiyama. 1977. Security Prices and Rates of Inter-est in Japan: 1874–1975. Tokyo: Hitotsubashi University.
Gabaix, Xavier. 1999. “Zipf’s Law for Cities: An Explanation,” Quarterly Journalof Economics 114, no. 3: 739–67.
———. 2008. “Variable Rare Disasters: An Exactly Solved Framework for TenPuzzles in Macro-Finance.” Working Paper 13724. Cambridge, Mass.:National Bureau of Economic Research (January).
Gabaix, X., and Rustam Ibragimov. 2007. “Rank-1/2: A Simple Way to Improvethe OLS Estimation of Tail Exponents.” Technical Working Paper 342. Cam-bridge, Mass.: National Bureau of Economic Research (September).
80 Brookings Papers on Economic Activity, Spring 2008
11302-04_Barro.qxd 8/15/08 5:38 PM Page 80
Lucas, Robert E., Jr. 1978. “Asset Prices in an Exchange Economy.” Economet-rica 46, no. 6: 1429–45.
Maddison, Angus. 2003. The World Economy: Historical Statistics. Paris: Organi-zation for Economic Cooperation and Development.
Mandelbrot, Benoit. 1963. “The Variation of Certain Speculative Prices.” Journalof Business 36, no. 4: 394–419.
Mehra, Rajnish, and Edward C. Prescott. 1985. “The Equity Premium: A Puzzle.”Journal of Monetary Economics 15, no. 2: 145–61.
Rietz, Thomas A. 1988. “The Equity Risk Premium: A Solution.” Journal of Mon-etary Economics 22, no. 1: 117–31.
Romer, Christina D. 1986. “Is the Stabilization of the Postwar Economy a Figmentof the Data?” American Economic Review 76, no. 3: 314–34.
Taylor, Bryan. 2005. “GFD Guide to Total Returns on Stocks, Bonds and Bills.”Los Angeles: Global Financial Data. www.globalfinancialdata.com/articles/total_return_guide.doc
Ursúa, J. F. 2008. “The 1921 World Recession: Was it World War I or the Flu?”Harvard University.
Weil, Philippe. 1990. “Nonexpected Utility in Macroeconomics.” Quarterly Jour-nal of Economics 105, no. 1: 29–42.
Weitzman, Martin L. 2007. “Subjective Expectations and Asset-Return Puzzles.”American Economic Review 97, no. 4: 1102–30.
ROBERT J. BARRO and JOSÉ F. URSÚA 81
11302-04_Barro.qxd 8/15/08 5:38 PM Page 81
82
Comments and Discussion
COMMENT BY
OLIVIER J. BLANCHARD Even if one is not deeply interested in theequity premium puzzle, this paper by Robert Barro and José Ursúa willprove extremely useful. Understanding the economic implications of dis-asters, whether natural or man-made, is both essential and fascinating.Like the celebrated Barro-Lee growth dataset, the dataset that the authorshave carefully put together for this project will be widely used. I had funplaying with it, and so will others.
I shall organize my comments around two points. The first is that macro-economic crises—what the authors call consumption and GDP disasters—come in very different forms, with different implications for output,consumption, and rates of return on bills, bonds, and stocks. The second isthat if the focus is on the equity premium, and if one takes seriously theclaim that the authors have now provided a representative sample of disas-ters, then looking at the determination of the equity premium through thelens of the Lucas model does not seem the best way to proceed.
THE MANY INCARNATIONS OF CONSUMPTION DISASTERS What I was moststruck by, looking at the consumption disasters identified and documentedby the authors, was how different these disasters in fact were one fromanother. As I went through the list, it became fairly clear that the disastersshould be put in different boxes. Here is a tentative breakdown.
Wars on one’s own soil. For obvious reasons, a war on one’s own soilleads to a large decline in output and consumption. Part of the country isoccupied by the enemy, and production in the rest is seriously disrupted.
I thank Antoine Bozio for information about the French stock market, Pedro Portugalfor information about the Portuguese stock market, and the authors for providing me withtheir data.
11302-04_Barro.qxd 8/15/08 5:38 PM Page 82
The stock market, if it remains open, does poorly. Depending on the extentof rationing, inflation may be high; real bill returns are likely to be low.
A good example is France during World War II. From 1937 to 1944,output per capita in France decreased by 51 percent (using log differ-ences); not until 1947 did it return to its 1937 level. From 1938 to 1943,consumption per capita decreased by 86 percent (this seems extremelylarge); not until 1949 did it return to its 1938 level.1
The German invasion closed the stock market. It reopened under theVichy regime, but, not surprisingly, volume remained very low during thewar.2 (This raises the issue of what one should assume for stock returnswhen the market is closed. Could one reasonably argue that if one cannotsell one’s stock, the rate of return in such years is −100 percent?) Leaving1940 and 1941 aside, the average yearly rate of return on stocks from 1938to 1947 was −10 percent.
Despite widespread rationing, average inflation in France during thewar was high. From 1938 to 1944, annual inflation as measured by the con-sumer price index averaged 18.7 percent, leading to large negative bill andbond returns. (Rationing also raises the issue of whether it makes sense touse the first-order condition of consumers. This condition relies on athought experiment in which a larger return on the asset allows one toincrease consumption at the margin, but such an increase may not feasibleunder rationing.) As is often the case, the immediate postwar period wasassociated with a burst of inflation, leading to even larger negative bill andbond returns. Inflation from 1945 to 1948 averaged 58.7 percent, and billand bond returns were negative and very large.
Wars on foreign soil. Wars on foreign soil have a very different eco-nomic profile. With the increase in defense spending, output is likely toincrease, but its composition is likely to change drastically. Whetherthrough rationing or through other means, consumption is likely to fall.After the initial bad news that a war is imminent, the stock market, pushedby defense stocks, is likely to do well. Depending on the form of rationingand the extent of forced saving, inflation is likely to rise, while nominalrates of return are kept low, leading to negative real bond returns.
The standard example here is the United States during World War II.From 1941 to 1945, U.S. output per capita grew by 34 percent. Consumptionper capita dipped by 3 percent from 1941 to 1942 but was still 5 percent
ROBERT J. BARRO and JOSÉ F. URSÚA 83
1. All the numbers on GDP, consumption, and stock and bond returns cited in this com-ment are from the Barro-Ursúa database.
2. The authors assume that it was closed during both 1940 and 1941. My French histo-rian friends tell me that it was closed only for a few weeks in 1940.
ftn. 1
ftn. 2
11302-04_Barro.qxd 8/15/08 5:38 PM Page 83
higher in 1945 than in 1941. The small consumption decrease in 1942 isnot large enough to make the authors’ “consumption disaster” list. Inter-estingly (and I return to this below), the United States does make the “GDPdisaster” list in the 1940s, but, perhaps surprisingly, for the period 1944 to1947, which includes the first two postwar years. The reason is the return ofthe U.S. economy from the wartime boom to a more normal level of output.
With the boom and the increase in defense spending, U.S. stock returnswere high during the war. From 1941 to 1945, annual stock returns aver-aged 12 percent; from 1942 to 1945, they averaged 20.9 percent. Despiteprice controls, inflation ran at an average 5 percent a year from 1941 to1945. Coupled with very low nominal interest rates aimed at limiting theburden of increasing government debt, the result was negative rates ofreturn on government bonds. As in France, the immediate aftermath of thewar was characterized by a burst of inflation, which reached 18 percent in1946, leading to large negative returns on nominal assets.
Civil wars. Civil wars offer yet another pattern of co-movements amongoutput, consumption, and stock and bond returns. A leftist revolution, forexample, may lead to an initial shift in income distribution and an initialincrease in consumption, followed later by lower output and lower con-sumption. Companies are likely to be nationalized, and stock returns arelikely to suffer. Loss of government revenue is likely to lead to rapidmoney growth, high inflation, and large losses on nominal assets.
Portugal provides a nice example. In 1974, after a long dictatorship andthe loss of Portugal’s colonies, a bloodless coup put leftist colonels incharge. Political and economic turmoil ensued, together with large-scalenationalization of firms. Although output decreased marginally from 1973to 1974, consumption increased by 7 percent (one may, however, reason-ably question whether the consumption of stockholders increased as well).The measured labor share of income exceeded 100 percent of GDP, and soit is no great surprise that both output and consumption declined in the fol-lowing years. Not until 1978 did they exceed their 1973 level.
Not surprisingly, the Portuguese stock market did not do well. The mar-ket was closed from April 1974 to February 1977. Measured stock returnswere negative and large in 1978. But bill returns did not fare much better.Inflation averaged 20 percent a year from 1974 to 1978 and remainedabove 20 percent until 1985. Nominal interest rates were substantiallylower, implying large negative real returns.
Other types of crisis, and some implications, One could go on. Anotherbox would include fiscal crises. Fiscal crises accompanied by hyperinfla-tions are likely to feature low output and low consumption. Stock returns
84 Brookings Papers on Economic Activity, Spring 2008
11302-04_Barro.qxd 8/15/08 5:38 PM Page 84
may be dismal, but so are bill and bond returns. Here the German hyper-inflation of 1923 is the obvious example. During this consumption disaster,as defined by the authors’ dates, stock prices declined by 65.4 percent. Butthe real rate of return on bills was −97 percent. Another box would includebanking crises, such as that in Finland in the early 1990s, and so on.
In going through these cases, I have done what Barro and Ursúa pre-cisely do not want us to do. I have tried to think about each data point andtold a specific story. The authors’ interest is in general patterns and theuse of a large sample of disasters to uncover them. This makes sense,however, only if all these disasters are realizations from the same under-lying process. This seems unlikely. Conditioning on the probability of awar at home will not imply the same set of conditional correlations asconditioning on a war fought abroad; they imply very different patternsof correlations. And if the probabilities of these different events varyacross countries and time, the implications of an unconditional approachare likely to be misleading.
To take an example, and venturing further than I should, it is likely thatin the United States the probability of a war at home (say, the explosion ofan atomic bomb) has decreased with the end of the cold war (conventionalterrorism, including the use of “dirty” bombs, is unlikely to create disasterson the same scale). But one may argue that the probability of a war abroadhas increased. One may also argue that the probabilities of a hyperinflationor a financial crisis have changed substantially over time. If this is the case,then the unconditional equity premium derived by the authors is likely tobe misleading.
DO WE NEED THE LUCAS-TREE MODEL? Having collected their data, Barroand Ursúa analyze the data through the lens of a Lucas-tree model, aug-mented for a small annual probability of disaster à la Thomas Rietz. Thisrequires them to estimate the probability of a disaster, p, and the size of therelative consumption disaster, b.
I do not understand why the authors force themselves to look at the datathrough this particular straightjacket. Doing so forces them to choose datesfor the start and the end of each disaster, to ignore the length of the disas-ter, to make assumptions about returns on bills, and so on. The way inwhich they map the data onto the inputs of the model is sensible, and giventhe mapping constraint, they do the best job that one can, but the results aresometimes surprising. The choice, for example, of a peak-to-trough frac-tional decline larger than 10 percent as a criterion for consumption or GDPdisasters seems perfectly reasonable. But it leads, for example, to defininga consumption disaster for France from 1938 to 1943, even though con-
ROBERT J. BARRO and JOSÉ F. URSÚA 85
11302-04_Barro.qxd 8/15/08 5:38 PM Page 85
sumption remained below its 1938 value until 1949. (Recall that the highinflation and very low bill returns occurred from 1945 to 1948, thus afterthe authors’ consumption disaster, but before consumption returned to itsprewar level. This may be relevant to the way one thinks about asset pric-ing.) It also leads to defining a GDP disaster for the United States from1944 to 1947, which might have come as a surprise to participants at thetime. Given a mechanical rule, one has to accept the discipline of the rule,and the consequences. The question is whether the rule is needed.
The motivation for using the Lucas-Rietz model until now was twofold.The first was to clarify the potential role of low-probability events in assetpricing; the model is at just the right level between simplicity and complex-ity to give nontrivial insights. The second was that researchers lacked evena representative sample, much less a universe, of disasters to analyze. Thusone could not be too ambitious in describing correlations during crises, andthe simple p and b approach seemed properly humble and transparent.
The point of this paper is, however, to provide a much larger sample,indeed the universe of consumption disasters that one can hope to measure.In this case I see no reason not to go back to asset pricing formulas thatrely only on the first-order intertemporal condition of consumers with noadditional assumptions. As is well known, this simplified condition can bewritten, for any asset, as
where M is the marginal rate of substitution between consumption todayand consumption in the next period, R is the gross rate of return on theasset—stocks, bills, or bonds—over the same period, and E(.) is a condi-tional expectation.
Given a specification of utility and thus of the marginal rate of substitu-tion, that condition can be used to compute conditional or unconditionalrequired returns on stocks, bills, and bonds and the implied equity pre-mium. This computation does not require taking a stand on starting andending dates for consumption disasters, nor does it require treating bills asriskless. It deals naturally with issues of disaster length, which are centralto the computation in the Lucas-Rietz framework. It allows one to explorehow the bursts of inflation that often follow consumption disasters are rel-evant to the equity premium. In short, it seems to simplify the task and toget around a number of the issues that arise under the current formaliza-tion. I hope the authors explore this route in the future.
E ER M M R( ) = ( )[ ] − ( )[ ]1 1 cov , ,
86 Brookings Papers on Economic Activity, Spring 2008
11302-04_Barro.qxd 8/15/08 5:38 PM Page 86
COMMENT BY
GEORGE M. CONSTANTINIDES An important contribution of thispaper by Robert Barro and José Ursúa is the compilation of a comprehen-sive database of real growth in consumption per capita for twenty-fourcountries and in GDP per capita for thirty-six, with data for some countriesdating back to 1870. This database builds upon and greatly expands an ear-lier one by Angus Maddison on GDP growth and is, in its own right, aninvaluable resource for future research.1
The paper’s second contribution is to employ this database to revisit andexpound on earlier investigations by Thomas Rietz and by Barro himselfin understanding the role of rare but major economic disasters in the equitypremium and the risk-free rate puzzles.2 My discussion focuses on the lat-ter contribution.
The equity premium puzzle, to use the term coined by Rajnish Mehraand Edward Prescott,3 originally referred to the inability of the standardneoclassical economic theory to reconcile the historically large realizedpremium of stock market returns over the risk-free interest rate with its lowcovariability with aggregate consumption growth.4 By now it is recognizedthat the challenge is actually a dual puzzle of the historical equity premiumbeing too high (the equity premium puzzle) and the risk-free rate being toolow (the risk-free rate puzzle), relative to the model predictions. The
ROBERT J. BARRO and JOSÉ F. URSÚA 87
1. Angus Maddison, The World Economy: Historical Statistics (Paris: Organization forEconomic Cooperation and Development, 2003).
2.Thomas A. Rietz, “The Equity Risk Premium: A Solution,” Journal of Monetary Eco-nomics 22, no. 1 (1988): 117–31; Robert J. Barro, “Rare Disasters and Asset Markets in the Twentieth Century,” Quarterly Journal of Economics 121, no. 3 (2006): 823–66. Relatedpapers include Jean-Pierre Danthine and John B. Donaldson, “Non-Falsified Expecta-tions and General Equilibrium Asset Pricing: The Power of the Peso,” Economic Jour-nal 109, no. 458(1999): 607–35; Xavier Gabaix, “Variable Rare Disasters: An Exactly SolvedFramework for Ten Puzzles in Macro-finance,” working paper, New York University, 2007; Christian Julliard and Anisha Ghosh, “Can Rare Events Explain the Equity Premium Puz-zle?” working paper, London School of Economics, 2008; and Rajnish Mehra and EdwardC. Prescott, “The Equity Premium: A Solution?” Journal of Monetary Economics 22, no. 1(1988): 133–36.
3. Rajnish Mehra and Edward C. Prescott, “The Equity Premium: A Puzzle,” Journalof Monetary Economics 15, no. 2 (1985): 145–61.
4. Early references include Sanford J. Grossman and Robert J. Shiller, “The Determi-nants of the Variability of Stock Market Prices,” American Economic Review 71, no. 2(1981): 222–27; Lars Peter Hansen and Kenneth J. Singleton, “Generalized InstrumentalVariables Estimation of Nonlinear Rational Expectations Models,” Econometrica 50, no. 5(1982): 1269–86; and Philippe Weil, “The Equity Premium Puzzle and the Risk-Free RatePuzzle,” Journal of Monetary Economics 24, no. 3 (1989): 401–21.
ftn. 1-4
11302-04_Barro.qxd 8/15/08 5:38 PM Page 87
research agenda has subsequently been expanded to encompass a numberof empirical regularities in the prices of capital assets that are at odds withthe predictions of standard economic theory, notably that the returns ofvarious subclasses of financial assets are too large, too variable, and toopredictable.5 Several generalizations of essential features of the modelhave been proposed to mitigate its poor performance.6
In particular, Rietz entertained the possibility that rare but major eco-nomic disasters cause a large decline in consumption per capita. In theory,the prospect of such disasters gives rise to a significant equity premium,while leaving the risk-free rate low because of the precautionary demandfor savings. Rietz calibrated economies that matched both the moments ofthe time-series process of consumption growth and the unconditional meanof the equity premium and the risk-free rate. He pointed out that the size ofthe annual (negative) consumption growth at the onset of an economicdisaster needed to resolve the puzzle in his calibrated economies is of thesame order of magnitude as the (negative) consumption growth over theentire Great Depression. He also pointed out that the model explains onlya small fraction of the equity premium if one calibrates the annual (nega-tive) consumption growth at the onset of an economic disaster to annualconsumption growth over the Great Depression.7 Rietz’s model fell by thewayside until recently revived by Barro.8
The thesis in that paper and in the present one is that a more careful cal-ibration of the model implies that major economic disasters explain most
88 Brookings Papers on Economic Activity, Spring 2008
5. This extensive literature is reviewed in a collection of essays edited by RajnishMehra, Handbooks in Finance: Handbook of the Equity Risk Premium (Amsterdam: Else-vier, 2008); in textbooks by John Y. Campbell, Andrew W. Lo, and A. Craig MacKinlay,The Econometrics of Financial Markets (Princeton University Press, 1997) and by J. H.Cochrane, Asset Pricing (Princeton University Press, 2005); and in several articles, includ-ing John Y. Campbell, “Consumption-Based Asset Pricing,” in Handbook of the Economicsof Finance, vol. IB: Financial Markets and Asset Pricing, edited by George M. Constanti-nides, Milton Harris, and Rene Stulz, Handbooks in Economics vol. 21 (Amsterdam: North-Holland, 2003); John H. Cochrane and Lars Peter Hansen, “Asset Pricing Explorations forMacroeconomics,” NBER Macroeconomics Annual 7 (1992): 115–65; George M. Constan-tinides, “Rational Asset Prices”; and Rajnish Mehra and Edward C. Prescott, “The EquityPremium in Retrospect,” in Handbook of the Economics of Finance, vol. IB: Financial Mar-kets and Asset Pricing.
6. These include idiosyncratic income shocks in incomplete markets; alternativeassumptions about preferences; distorted beliefs and learning; market imperfections; liquid-ity risk; better understanding of data problems such as limited participation of consumers inthe stock market; temporal aggregation; regime shifts; and the survival bias of the U.S. cap-ital market.
7. Barro, “Rare Disasters and Asset Markets in the Twentieth Century.” See also thediscussion in Mehra and Prescott “The Equity Premium: A Solution?”
8. Barro, “Rare Disasters and Asset Markets in the Twentieth Century.”
ftn. 5-8
11302-04_Barro.qxd 8/15/08 5:38 PM Page 88
of the observed equity premium. Barro and Ursúa’s central argument isthat one should calibrate the consumption decrease over the first year ofthe disaster to the measured cumulative consumption decrease from peakto trough of the disaster period. They motivate this approach with theobservation that the incidence of negative shocks to consumption growthincreases upon the onset of the economic disaster. Although I recognizethe validity of their observation, I explain below why I disagree with theircalibration and conclude that a correctly calibrated model, such as that ofRietz, explains only a small fraction of the observed premium.
Before I describe the specifics of the authors’ model and discuss it indetail, let me explain in broad terms why I disagree with their central argu-ment. I begin, as they do, with the standard neoclassical economic model,as adapted in finance. In a single-good economy, the representative con-sumer chooses consumption plan {Ct}t=0,1, . . ., subject to a budget con-
straint, and maximizes expected utility with a constant
relative risk aversion coefficient γ and a subjective discount factor β.9 LetRj
t,t+1be the total return on the jth asset from time t to time t + 1. If (Ct, Ct+1)
is the optimal consumption plan at times t and t + 1, then the feasibleconsumption plan (Ct − δ, Ct+1 + δRj
t,t+1) maximizes expected utility with
respect to δ at δ = 0, where δ is saving in period t. This variational argu-ment leads to the standard Euler equation of consumption between times tand t + 1,
as in the authors’ equation 4.Suppose that time t signifies the onset of an economic disaster. Then the
Euler equation between times t and t + 1 depends on the conditional distri-bution of consumption growth at time t, Ct+1/Ct, between times t and t + 1and on total return, Rj
t,t+1, between times t and t + 1. Note that this deriva-tion remains valid even if the consumption growth series, Ct+1/Ct, Ct+2/Ct+1, . . . , is autocorrelated.
( ) ,,1 111E
C
CRt
t
t
t tjβ
γ
+
−
+
⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢⎢
⎤
⎦⎥⎥=
E Ct tt01
0β γ−
=
∞∑⎡⎣ ⎤⎦
ROBERT J. BARRO and JOSÉ F. URSÚA 89
9. Barro and Ursúa also entertain Epstein and Zin preferences; see Larry G. Epsteinand Stanley E. Zin, “Substitution, Risk Aversion, and the Temporal Behavior of Consump-tion and Asset Returns: An Empirical Analysis,” Journal of Political Economy 99, no. 2(1991): 263–86. Their Euler equation 4 holds with Epstein-Zin preferences only if con-sumption shocks are i.i.d. However, Barro and Ursúa assume that, upon the onset of an eco-nomic disaster, the shocks are correlated. For their Euler equation 4 to remain valid, it isnecessary to limit discussion to utility ∑∞
t=0βtC1−γt .
ftn. 9
11302-04_Barro.qxd 8/15/08 5:38 PM Page 89
By contrast, Barro and Ursúa argue that upon the onset of an economicdisaster, annual consumption growth over the peak-to-trough period of thedisaster is highly autocorrelated and that one should replace one-year con-sumption growth, Ct+1/Ct, in the standard Euler equation with the measuredcumulative consumption decrease from peak to trough, for example,Ct+4/Ct for a four-year decline, as
This is the Euler equation that Barro and Ursúa implicitly apply upon theonset of an economic disaster. They provide no formal derivation of equa-tion 2, and I believe that this equation is incorrect. In a technical sense, thisEuler equation concentrates and magnifies the effect of an economic disas-ter and thus generates a much higher premium than equation 1 does (anobservation made earlier by Rietz).
The correct version of the Euler equation with the measured cumula-tive consumption decrease from peak-to-trough (four-year) consumptiongrowth, Ct+4/Ct, is
This equation states that the Euler equation on four-year consumptiongrowth addresses the four-year return.
As I will show later, the authors’ baseline consumption case (the firstrow in their table 10) says that their model of economic disasters generatesa premium of 0.059 − 0.01, or 4.9 percent, over 3.6 years. However, thehistorical equity premium over a holding period of 3.6 years is approxi-mately 3.6 × 6 percent = 21.6 percent.10 Thus, the authors’ model of eco-nomic disasters explains 4.9 ÷ 21.6 ≈ 0.227, or less than a quarter, of thehistorical equity premium.
Let me now turn to the authors’ formal model. Each year the economyis in either a normal state (N) or a disaster state (D). The sequence of statesat the annual frequency is a Markov chain. The transition probability inone year from N to D is p (and that from N to N is 1 − p); the transitionprobability in one year from D to N is π (and that from D to D is 1 − π).
( ) .,3 144E
C
CRt
t
t
t tjβ
γ
+
−
+
⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢⎢
⎤
⎦⎥⎥=
( ) .,2 141E
C
CRt
t
t
t tjβ
γ
+
−
+
⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢⎢
⎤
⎦⎥⎥=
90 Brookings Papers on Economic Activity, Spring 2008
10. See, for example, George M. Constantinides, “Rational Asset Prices,” Journal ofFinance 57 (August 2002): 1567–91, for estimates of the historical equity premium.
ftn. 10
11302-04_Barro.qxd 8/15/08 5:38 PM Page 90
One easily calculates the unconditional probability of a year being in stateN as PN = π/(π + p) and that of being in state D as PD = p/(π + p). Theannual probability of the onset of a disaster is π × p/(π + p), and theexpected length of a disaster is π−1 years.
In their baseline case, Barro and Ursúa observe that the sample meanlength of disasters is 3.6 years. Therefore, I set π = (3.6)−1 = 0.278, whichagrees with their value of 0.277 in table 10. They observe 343 disaster-years out of a total of 2,963 years across countries. Therefore, I set theunconditional probability of a disaster year as PD = p/(π + p) = 343/2,963 =0.1158, which, combined with π = 0.278, gives p = 0.0364. This value of pis approximately equal to the authors’ value of 0.0363 in table 10. Thus,the authors and I are in agreement regarding the calibration of the Markovchain in the baseline case.11
Note that the Markov chain and its calibration already accommodate theobservation that the incidence of consumption growth shocks is highlycorrelated during a disaster: whereas the unconditional probability of adisaster year is PD = 0.1158, the probability conditional on the previousyear being a disaster year is 1 − π = 1 − 0.278 = 0.722. I argue later on thatBarro and Ursúa double-count this correlation.
Barro and Ursúa assume the following process for annual consumptiongrowth:
where ut+1, υt+1 are i.i.d., ut+1 ∼ N(0, σ2), υt+1 = 0 if t + 1 is a normal year, andυt+1 = log(1 − b) if t + 1 is a disaster year. If t is a normal year, then theprobability that t + 1 is a normal year is 1 − p, and the probability that it isa disaster year is p; if t is a disaster year, then the probability that t + 1 is anormal year is π, and the probability that it is a disaster year is 1 − π. Thus,Barro and Ursúa model annual consumption growth as a process that is noti.i.d., contrary to their claim: “However, Barro shows that with i.i.d.shocks (as in the present model), the first-order optimizing conditions gen-erate asset pricing equations of familiar form.”
Barro and Ursúa set the probability that ut+1 = log(1 − b) equal to p =0.0363 in the baseline. Recall, however, that p was earlier defined as thetransition probability in one year from N to D. The probability that υt+1 =log(1 − b) should be set equal to the unconditional probability of a disasteryear, PD = p/(π + p) = 0.1158.
( ) log log ,4 1 1 1C C g ut t t t+ + +− = + + υ
ROBERT J. BARRO and JOSÉ F. URSÚA 91
11. Note that this calibration does not account for estimation error and, in particular, thecorrelation of economic disasters across countries.
ftn. 11
11302-04_Barro.qxd 8/15/08 5:38 PM Page 91
A critical issue is the size of the annual consumption growth shock in adisaster year, υt+1 = log(1 − b). Barro and Ursúa assume that the peak-to-trough shock occurs in the first year of a disaster. This assumption is notsupported by the data over the two primary consumption disaster periodsin the United States, 1917–21 and 1929–33. Over 1917–21, the arithmeticannual total real consumption growth, [(Ct+1/Ct) − 1] × 100, is −2.6 per-cent, −3.7 percent, −4.6 percent, and −6.4 percent in 1917–18, 1918–19,1919–20, and 1920–21, respectively.12 The most important feature of thesedata is that the consumption decline in the first year of the disaster periodis the smallest annual decline over the 1917–21 period and accounts foronly a fraction of the total consumption decline. Likewise, over the period1929–33 the arithmetic annual total consumption growth, [(Ct+1/Ct) − 1] ×100, is −6.4 percent, −3.9 percent, −9.5 percent, and −2.8 percent in 1929–30, 1930–31, 1931–32, and 1932–33, respectively. As before, the con-sumption decline in the first year of the disaster period accounts for only afraction of the total consumption decline. Similar observations apply todata on nondurables consumption. These observations do not support theauthors’ calibration that treats the peak-to-trough consumption decline asif it occurs in the first year of the disaster period.
Given the above observations and the Markovian nature of the authors’model, I proceed to calibrate the fractional decline in annual consumptionb if the end of the year is a disaster year. The expected cumulative peak-to-trough consumption ratio is
For this calculation I rely on the authors’ assumption that the shocks (1 − b1),(1 − b2), . . . , (1 − bn) are i.i.d.
( ) . . .5 1 1 1 11
1 21
E b b bn
nn
π π−( ) −( ) −( ) −( )⎡⎣⎢
⎤−
=
∞
∑ ⎦⎦⎥
= −( ) −( )
=−( )
− −( ) −( )
−
=
∞
∑π π
ππ
1 1
1
1 1 1
1
1
n n
n
b
b
b..
92 Brookings Papers on Economic Activity, Spring 2008
12. In private communication, the authors kindly provided the data for total consump-tion growth and nondurables consumption growth over 1917–21 and 1929–33. I draw similarconclusions by using consumption data on nondurables and services from John Campbell’swebsite (www.economics.harvard.edu/faculty/campbell) and by using consumption datafrom Robert Shiller’s website (www.econ.yale.edu/∼shiller/data.htm) that include durablesin the definition of consumption.
ftn. 12
11302-04_Barro.qxd 8/15/08 5:38 PM Page 92
In the authors’ baseline case, they assume that the expected cumulativetrough-to-peak consumption ratio is 1 − 0.219 = 0.781. Setting π(1 − b
–)/
[1 − (1 − π)(1 − b–
)] = 0.781 and π = 0.278, I obtain 1 − b– = 0.928. As a
back-of-the-envelope calculation, note that with the sample mean length ofdisasters being 3.6 years, the expected cumulative trough-to-peak con-sumption ratio is roughly (0.928)3.6 = 0.764, which is very close to 0.781.
Barro and Ursúa assume for convenience that “equity” or the “stockmarket” is the claim to the future consumption stream. Effectively, theyassume that the capitalized value of future labor income is either zero or included in “equity.” This assumption conveniently allows one to bypassthe need to specify the conditional return distribution on the equity.Although this assumption is counterfactual, it is a common assumption inthe early literature on the equity premium and I leave it at that.
Barro and Ursúa state the Euler equation of consumption between datest and t + 1 for the equity return and the risk-free rate in their equations 6and 7, respectively. I take the difference of these equations and obtain thepremium as follows:
If b were constant, equation 6 would simplify to r e − r f = γσ2 +p{b[E(1 − b)−γ − 1]}. This is the same as equation 8 in the paper. However,the authors do not assume that b is constant, and therefore their equation 8is incorrect.
Even after this correction, another correction needs to be made in myown equation 6. Based on my discussion above, I correct equation 6 byreplacing p with p/(π + p), the unconditional probability of a disaster stateat the end of the year, and state it as follows:
As I argued above, 1 − b should be thought of as the one-year consumptionratio in disaster years and not as the cumulative trough-to-peak consump-tion ratio in these years. Since I do not have the moments for E(1 − b)−γ andE(1 − b)1−γ either over one year or over the cumulative trough-to-peakperiod, I do a calibration in the special case where b is constant. The pointof this exercise is to demonstrate that the authors’ approach and mine yieldresults that differ by an order of magnitude, when in both cases b is treatedas constant. In both cases I set γ = 3.5, p = 0.0363, and π = 0.278 and sup-press the term γσ2, as the authors do.
( )7 1 121
r rp
E b E b Ebe f− = ++( ) −( ) − −( ) −⎡⎣ ⎤− −γσ
π ργ γ
⎦⎦.
( ) .6 1 121
r r p E b E b Ebe f− = + −( ) − −( ) −⎡⎣ ⎤⎦− −γσ γ γ
ROBERT J. BARRO and JOSÉ F. URSÚA 93
11302-04_Barro.qxd 8/15/08 5:38 PM Page 93
First, I consider the authors’ approach. When I set 1 − b = 0.781, equa-tion 7 yields an annual equity premium re − r f = 0.0348. By contrast, whenI set 1 − b = 0.928, which I argued is the correct way to think about theannual shock in a disaster state, equation 7 yields an annual equity pre-mium re − r f = 0.0025. Although both numbers are small because I havesuppressed uncertainty about b for reasons of convenience, the point is thatthe premium 0.0025 is less than one-tenth of the premium 0.0348. I rec-ommend that the authors provide the annual moments for E(1 − b)−γ andE(1 − b)1−γ and repeat the above comparison without the assumption that bis constant.
As I argued above, there is an alternative and intuitive way to makethe same point. I finesse the controversial issue as to whether the entireshock to consumption occurs in the year of onset of the disaster or is dis-tributed over all years of the disaster, by choosing the length of oneperiod in the model to be 3.6 years instead of one year. In this case itdoes not matter which year during the disaster period is the year in whichconsumption drops. Then the baseline case in the authors’ table 10 saysthat their model of economic disasters generates a premium of 0.059 −0.01, or 4.9 percent, over 3.6 years. However, the historical equity pre-mium over a holding period of 3.6 years is, as noted above, approxi-mately 3.6 × 6 = 21.6 percent, which again is less than a quarter of thehistorical equity premium.
Barro and Ursúa do not provide empirical evidence to support givingspecial status to one year as the length of time over which the entire shockto consumption occurs upon the onset of a disaster. Had they insteadpicked one month as the critical period, the modified calibration abovewould predict a one-month premium of 4.9 percent, which is almost tentimes the historical one-month premium of 6⁄12 = 0.5 percent.
I have argued that Barro and Ursúa do not deliver a convincingly cali-brated model of economy-wide disasters that explains a substantial frac-tion of the historically observed equity premium. The reason is that theannual drop in consumption during these disasters is too small to explainthe premium, even after allowing for the fact that the incidence of negativeshocks to consumption growth increases upon the onset of an economicdisaster. The authors’ device of attributing the entire peak-to-trough dropin consumption to the year of onset of the disaster is simply counterfactualand double-counts the increased incidence of negative shocks to consump-tion growth after the onset of the disaster. In a recent empirical study,Christian Julliard and Anisha Ghosh find that economy-wide disasters,
94 Brookings Papers on Economic Activity, Spring 2008
11302-04_Barro.qxd 8/15/08 5:38 PM Page 94
along the lines of Barro’s 2006 paper and the present one, do not explainthe cross section of asset returns.13
There is, however, an alternative interpretation of economic disasters,namely, as periods where the incidence of large negative idiosyncraticincome shocks increases at the household level.14 These shocks maylargely wash out at the aggregate level and may not even show up in aggre-gate consumption data. Nevertheless, these shocks potentially play a majorrole in the pricing of financial assets through the household Euler equa-tions of consumption, provided they are persistent and uninsurable. Giventhat markets provide grossly incomplete consumption insurance, models thataccount for these shocks show promise for understanding the source of theequity premium and of the premiums I think the plural of premium is pre-mia of subclasses of financial assets.
ROBERT J. BARRO and JOSÉ F. URSÚA 95
13. Julliard and Ghosh, “Can Rare Events Explain the Equity Premium Puzzle?” work-ing paper, London School of Economics.
14. Such models were suggested by Mehra and Prescott in an early draft of their 1985paper, “The Equity Premium: A Puzzle,” working paper, Carnegie-Mellon University, 1980;and by N. Gregory Mankiw, “The Equity Premium and the Concentration of AggregateShocks,” Journal of Financial Economics 17, no. 1 (1986): 211–19. George M. Constanti-nides and Darrell. Duffie, “Asset Pricing with Heterogeneous Consumers,” Journal of Polit-ical Economy 104, no. 2 (1996): 219–40, introduced such a model in an intertemporaleconomy. Alon Brav, George M. Constantinides, and Christopher C. Geczy, “Asset Pricingwith Heterogeneous Consumers and Limited Participation: Empirical Evidence,” Journal ofPolitical Economy 110, no. 4 (2002): 793–824, provided empirical support for the model.See also Tom Krebs, “Testable Implications of Consumption-Based Asset Pricing Modelswith Incomplete Markets,” Journal of Mathematical Economics 40, no. 1–2 (2004):191–206.
ftn. 13
ftn. 14
11302-04_Barro.qxd 8/15/08 5:38 PM Page 95
11302-04_Barro.qxd 8/15/08 5:38 PM Page 96